Chapter 1: Logic and Proof
Propositional Logic Semantics
Propositional variables: p, q, r, s, ... (stand for simple sentences)
T: any proposition that is always true
F: any proposition that is always false
Compound propositions: formed from propositional variables and logical operators (all binary except negation):
Negation ¬
Conjunction ∧
Disjunction ∨
Implication →
Biconditional ↔
Exclusive Or ⊕
Truth Tables: assign all possible T, F to all possible variables, and determines all possible T, F of compound propositions; with n variables there are 2n rows in the table
Negation changes T to F and vice versa
Conjunction is only T if both conjuncts are T
Disjunction is only F is both disjuncts are F
Implication is only F is the antecedent is T and the consequent is F
Biconditional is only true if they have the same tvalue
Exclusive Or is only T if they differ in tvalue
Two (compound) propositions are equivalent (≡) iff they always have the same tvalue (see also below)
English translations:
Conjunction: and, but, although, yet, still, ...
Disjunctions: or, unless
Implication: if, if ... then, only if, when, implies, entails, follows from, is sufficient, is necessary, when, whenever
Biconditional: if and only if, just in case, is necessary and sufficient
A set of propositions is consistent iff there is some assignment of tvalue that makes all T
A set of propositions is inconsistent iff there is no assignment of tvalue that makes all T
A tautology is a compound propositions that is always T
A contradiction is a compound propositions that is always F
A contingency is a compound propositions that is sometimes T, sometimes F
A compound proposition is satisfiable iff some assignment of tvalues make it T
A compound proposition is unsatisfiable iff no assignment of tvalues make it T
Two compound propositions p and q are logically equivalent iff p ↔ q is a tautology
Common equivalences:
DeMorgan’s Laws (Dem)
¬(p ∨ q)≡¬p ∧ ¬q
¬(p ∧ q)≡¬p ∨ ¬q
Identity Laws (Id)
p ∧ T ≡p
p ∨ F ≡p
Domination Laws (Dom)
p ∨ T ≡T
p ∧ F ≡F
Idempotent Laws (Idem)
p ∨ T ≡T
p ∧ p ≡p
Double Negation Law (DN)
¬(¬p) ≡ p
Negation Laws (Neg)
p ∨ ¬p ≡T
p ∧ ¬p ≡F
Commutative Laws (Comm)
p ∨ q ≡q ∨ p
p ∧ q ≡q ∧ p
Associative Laws (Assoc)
(p ∨ q) ∨ r ≡p ∨ (q ∨ r)
(p ∧ q) ∧ r ≡p ∧ (q ∧ r)
Distributive Laws (Dist)
p ∨ (q ∧ r) ≡
(p ∨ q) ∧ (p ∨ r)
p ∧ (q ∨ r) ≡
(p ∧ q) ∨ (p ∧ r)
Absorption Laws (Abs)
p ∨ (p ∧ q) ≡ p
p ∧ (p ∨ q) ≡ p
Conditional Laws (Cond)
p →q≡ ¬p ∨ q
¬(p →q)≡ p ∧ ¬q
Biconditional Law (Bicond)
p ↔ q ≡ (p →q) ∧ (q →p)
Quantifier Negation (QNeg)
¬ ∀x P ( x ) ≡ ∃x ¬ P ( x )
¬ ∃x P ( x ) ≡ ∀x ¬ P ( x )
Predicate and Relational Logic (Quantificational Logic, First Order Logic): Semantics
Variables: x, y, z, ...
Predicates/Relations, Propositional Functions: P(x), M(x), Q(x,y), S(x,y,z), ...
Constants: a, b, c, 0, -1, 4, Socrates, ...
Domain (U): set of things the variables range over
Propositional functions are neither T nor F; however, if all the variables are re ...
This document discusses logic and propositional logic. It covers the following topics:
- The history and applications of logic.
- Different types of statements and their grammar.
- Propositional logic including symbols, connectives, truth tables, and semantics.
- Quantifiers, universal and existential quantification, and properties of quantifiers.
- Normal forms such as disjunctive normal form and conjunctive normal form.
- Inference rules and the principle of mathematical induction, illustrated with examples.
The document discusses different methods of representing knowledge in artificial intelligence systems, including formal logic, production rules, and structured objects like semantic networks and frames. It provides examples of representing statements in propositional and predicate calculus, and how logic-based languages like Prolog can be used for knowledge representation and reasoning. Semantic networks are introduced as a way to organize knowledge representation in a graph-like structure similar to how human memory works.
This document provides an introduction to logic, including propositional logic and predicate calculus. It defines key concepts such as logical values, propositions, operators, truth tables, logical expressions, worlds, models, inference rules, quantification, and definitions. Propositional logic manipulates true and false values using operators like AND and OR. Predicate calculus extends this to allow predicates, constants, functions, and quantification over variables. Inference involves applying rules to derive new statements, but the search space grows too large to feasibly perform by hand.
Discrete mathematics Ch2 Propositional Logic_Dr.khaled.Bakro د. خالد بكروDr. Khaled Bakro
Discrete Mathematics chapter 2 covers propositional logic. A proposition is a statement that is either true or false. Propositional logic uses propositional variables and logical operators like negation, conjunction, disjunction, implication and biconditional. Truth tables are used to determine the truth value of compound propositions formed using these operators. Logical equivalences between compound propositions can be shown using truth tables or by applying equivalence rules.
This document discusses an alternative approach to logic called the logic of acceptance and rejection (AR4). It begins by outlining three views on logic: logical absolutism, relativism, and relative charity. It then introduces AR4, which treats logic as involving questions, answers, and speech acts of assertion and rejection. Under AR4, a proposition can be answered by either asserting or rejecting it in response to the questions of whether it is the case and whether it is not the case. This moves beyond the traditional view of logic as only involving truth. The document outlines the components of AR4 and how it represents logic using a four-valued semantics involving acceptance and rejection.
This document discusses logic and propositional logic. It covers the following topics:
- The history and applications of logic.
- Different types of statements and their grammar.
- Propositional logic including symbols, connectives, truth tables, and semantics.
- Quantifiers, universal and existential quantification, and properties of quantifiers.
- Normal forms such as disjunctive normal form and conjunctive normal form.
- Inference rules and the principle of mathematical induction, illustrated with examples.
The document discusses different methods of representing knowledge in artificial intelligence systems, including formal logic, production rules, and structured objects like semantic networks and frames. It provides examples of representing statements in propositional and predicate calculus, and how logic-based languages like Prolog can be used for knowledge representation and reasoning. Semantic networks are introduced as a way to organize knowledge representation in a graph-like structure similar to how human memory works.
This document provides an introduction to logic, including propositional logic and predicate calculus. It defines key concepts such as logical values, propositions, operators, truth tables, logical expressions, worlds, models, inference rules, quantification, and definitions. Propositional logic manipulates true and false values using operators like AND and OR. Predicate calculus extends this to allow predicates, constants, functions, and quantification over variables. Inference involves applying rules to derive new statements, but the search space grows too large to feasibly perform by hand.
Discrete mathematics Ch2 Propositional Logic_Dr.khaled.Bakro د. خالد بكروDr. Khaled Bakro
Discrete Mathematics chapter 2 covers propositional logic. A proposition is a statement that is either true or false. Propositional logic uses propositional variables and logical operators like negation, conjunction, disjunction, implication and biconditional. Truth tables are used to determine the truth value of compound propositions formed using these operators. Logical equivalences between compound propositions can be shown using truth tables or by applying equivalence rules.
This document discusses an alternative approach to logic called the logic of acceptance and rejection (AR4). It begins by outlining three views on logic: logical absolutism, relativism, and relative charity. It then introduces AR4, which treats logic as involving questions, answers, and speech acts of assertion and rejection. Under AR4, a proposition can be answered by either asserting or rejecting it in response to the questions of whether it is the case and whether it is not the case. This moves beyond the traditional view of logic as only involving truth. The document outlines the components of AR4 and how it represents logic using a four-valued semantics involving acceptance and rejection.
It covers knowledge representation techniques using propositional and predicate logic. It also discusses about the knowledge inference using resolution refutation process, rule based system and bayesian network.
The document discusses various concepts in predicate logic including:
1. Universal and existential quantification allow representing statements like "for all" or "there exists".
2. Syntax of first-order logic includes constants, variables, functions, predicates, and quantifiers.
3. A predicate is satisfiable if true for some values, valid if true for all values, and unsatisfiable if false for all values.
4. Negating quantifiers flips the quantifier and negates the predicate. Free variables can be substituted while bound variables cannot. Restrictions filter domains.
Transfers Principles Revisited with Choquet’s Lemma on Successive DifferencesMarc Dubois
This document discusses transfers principles and their relationship to the derivatives of utility functions. It presents Choquet's lemma relating successive differences of a function to the signs of its derivatives. The author proves that a social welfare function satisfies the transfers principle of order s+1 if and only if the (s+1)th derivative of the utility function has a particular sign. This characterizes different attitudes toward inequality based on the signs of higher-order derivatives. The paper also discusses when "numbers don't win" at higher transfer orders.
20220818151924_PPT01 - The Logic of Compound and Quantitative Statement.pptxssuser92109d
This document provides an overview of logic and mathematical concepts including:
- Definitions of statements, propositions, negation, conjunction, disjunction and their truth tables
- Logical equivalence and how to prove it using truth tables or theorems
- Conditional, biconditional, and quantified statements
- Valid and invalid arguments
- Predicates and applying quantifiers to write statements in symbolic form
- Truth conditions for universal and existential propositions
- References used to adapt the content are cited
Discrete Mathematics is a branch of mathematics involving discrete elements that uses algebra and arithmetic. It is increasingly being applied in the practical fields of mathematics and computer science. It is a very good tool for improving reasoning and problem-solving capabilities.
1. The document discusses universal quantification and quantifiers. Universal quantification refers to statements that are true for all variables, while quantifiers are words like "some" or "all" that refer to quantities.
2. It explains that a universally quantified statement is of the form "For all x, P(x) is true" and is defined to be true if P(x) is true for every x, and false if P(x) is false for at least one x.
3. When the universe of discourse can be listed as x1, x2, etc., a universal statement is the same as the conjunction P(x1) and P(x2) and etc., because this
Introduction to set theory by william a r weiss professormanrak
This chapter introduces a formal language for describing sets using variables, logical connectives, quantifiers, and the membership symbol. Formulas in this language are constructed recursively from atomic formulas using negation, conjunction, disjunction, implication, biconditional, universal quantification, and existential quantification. The key concepts of subformula and bound variable are also defined. This language will allow precise discussion of sets without ambiguities like those found in natural languages.
Prove asymptotic upper and lower hounds for each of the following sp.pdfwasemanivytreenrco51
Prove asymptotic upper and lower hounds for each of the following specified otherwise, assume
that in each case, T(n) = 1 (or any small constant) for small value You may assume that n = c^k
for some constant c that you choose. Make your bounds as tight as (No need to specify the
origin of your guess.) T(n0 = 8T(n/3) + n^1.83838383... T(n) = T(n - 1) = 1/n T(n) = 16T(n/2)
+ (n log n)^4. T(n) = 2T(n/2) + n/lg n. T(n) = T(n - 1) + T(n - 2) + 1 with base case of T(1) = 1
and T(2) = 2
Solution
A statement are often outlined as a declaratory sentence, or a part of a sentence, that\'s capable of
getting a truth-value, like being true or false. So, as an example, the subsequent area unit
statements:
George W. Bush is that the forty third President of the us.
Paris is that the capital of France.
Everyone born on Monday has purple hair.
Sometimes, a press release will contain one or a lot of alternative statements as elements.
contemplate as an example, the subsequent statement:
Either Ganymede may be a moon of Jupiter or Ganymede may be a moon of Saturn.
While the on top of sentence is itself a press release, as a result of it\'s true, the 2 elements,
\"Ganymede may be a moon of Jupiter\" and \"Ganymede may be a moon of Saturn\", area unit
themselves statements, as a result of the primary is true and therefore the second is fake.
The term proposition is typically used synonymously with statement. However, it\'s typically
accustomed name one thing abstract that 2 totally different statements with an equivalent which
means area unit each aforementioned to \"express\". during this usage, nation sentence, \"It is
raining\", and therefore the French sentence \"Il pleut\", would be thought-about to specific an
equivalent proposition; equally, the 2 English sentences, \"Callisto orbits Jupiter\" and \"Jupiter
is orbitted by Callisto\" would even be thought-about to specific an equivalent proposition.
However, the character or existence of propositions as abstract meanings continues to be a matter
of philosophical dispute, and for the needs of this text, the phrases \"statement\" and
\"proposition\" area unit used interchangeably.
Propositional logic, conjointly referred to as linguistic string logic, is that branch of logic that
studies ways that of mixing or neutering statements or propositions to create a lot of difficult
statements or propositions. change of integrity 2 easier propositions with the word \"and\" is one
common approach of mixing statements. once 2 statements area unit joined along side \"and\",
the advanced statement fashioned by them is true if and as long as each the element statements
area unit true. owing to this, associate argument of the subsequent kind is logically valid:
Paris is that the capital of France and Paris contains a population of over 2 million.
Therefore, Paris contains a population of over 2 million.
Propositional logic for the most part involves learning logical connectives like the words \"and\"
and \"or\" and therefo.
This document provides an overview of logic, proofs, and their applications. It begins with definitions of logic and logical operations like conjunction, disjunction, and negation. It then discusses different types of proofs like direct proofs, proof by contradiction, and proof by induction. Examples are provided to illustrate logical operations and different proof techniques. The document concludes by discussing two applications of logic and proofs - translating English sentences into logical statements and performing Boolean searches.
This document provides an overview of logic and proofs. It begins by defining logic as the study of correct reasoning, and discusses how logic is used in mathematics and computer science. Some key concepts introduced include:
- Propositions and truth values
- Logical connectives like AND, OR, NOT
- Truth tables for evaluating compound propositions
- Quantifiers like "for all" and "there exists"
- Propositional functions and their domains
- Types of proofs like direct proof, proof by contradiction, and mathematical induction
The document concludes by covering resolution proofs and the strong form of mathematical induction, which involves verifying a basis step and proving the induction step. Overall, it serves as an introduction to
Artificial Intelligence (AI) | Prepositional logic (PL)and first order predic...Ashish Duggal
The following are the topics in this presentation Prepositional Logic (PL) and First-order Predicate Logic (FOPL) is used for knowledge representation in artificial intelligence (AI).
There are also sub-topics in this presentation like logical connective, atomic sentence, complex sentence, and quantifiers.
This PPT is very helpful for Computer science and Computer Engineer
(B.C.A., M.C.A., B.TECH. , M.TECH.)
Discrete Mathematics covers fundamentals of logic including propositions, truth tables, logical connectives, and propositional equivalences. A proposition is a statement that is either true or false. Logical connectives such as "and", "or", "not" are used to combine propositions into compound statements. Truth tables are used to determine the truth value of compound propositions based on the truth values of the individual propositions. Logical equivalences show that two statements are logically equivalent even if written differently. Examples help illustrate key concepts such as tautologies, contradictions and using equivalences to prove statements.
This document presents an overview of Rossella Marrano's talk on a qualitative perspective on vagueness and degrees of truth. The talk explores representing vagueness through comparative judgments of truth between sentences, rather than precise numerical assignments. It proposes axioms for a binary relation between sentences based on one being "more true" than the other. Representation results show that real-valued truth functions can arise from satisfying the axioms. The approach aims to address objections that assigning precise numerical truth values replaces vagueness with artificial precision.
The document provides an introduction to formal logic. It discusses how to formulate valid arguments through propositional logic and syllogistic logic. Propositional logic uses truth tables to evaluate combinations of propositions and operators like negation and conjunction. Syllogistic logic examines implications of general statements using domains and categories. The key rules of inference for valid arguments are hypothetical syllogism, modus ponens, and modus tollens.
The document discusses deductive and inductive arguments. It provides examples of valid and invalid deductive arguments using categorical propositions and conditional premises. It also discusses inductive arguments, noting that inductive conclusions generalize from specific premises rather than necessarily following from them. The document then compares deductive and inductive arguments and discusses their uses in everyday life and mathematics. It concludes by introducing some common rules of inference for deductive arguments.
This document provides an overview of logic and proofs in discrete mathematics. It discusses topics such as:
- Propositions and truth tables
- Logical connectives like conjunction, disjunction, negation, implication, and equivalence
- Quantifiers like universal and existential
- Different types of proofs like direct proof, proof by contradiction, and mathematical induction
- Rules of inference for propositional and quantified logic
- Resolution proofs
The document serves as an introduction to fundamental concepts in logic that are important for mathematical reasoning and proof techniques.
The document provides an introduction to discrete structures and mathematical reasoning. It discusses key concepts like propositions, logical operators, quantification, and proof techniques. Propositions can be combined using logical operators like negation, conjunction, disjunction, etc. Quantifiers like universal and existential are used to represent statements about all or some elements. Mathematical reasoning involves using axioms, rules of inference, and deductive proofs to establish theorems from given conditions.
Mathematical argumentation as a precursor of mathematical proofNicolas Balacheff
Along history or across educational traditions, the space given to mathematical proof in compulsory school curricula varies from a quasi-absence to a formal obligation which for some has turned into an obstacle to mathematics learning. The contemporary evolution is to give to proof the space it deserves in the learning of mathematics. This is for example witnessed in different ways by The national curriculum in England (2014), the Common Core State Standards for Mathematics (2010) in the US or the recent Report on the teaching of mathematics (1918) commissioned by the French government; the latter asserts: The notion of proof is at the heart of mathematical activity, whatever the level (this assertion is valid from kindergarten to university). And, beyond mathematical theory, understanding what is a reasoned justification approach based on logic is an important aspect of citizen training. The seeds of this fundamentally mathematical approach are sown in the early grades. These are a few examples of the current worldwide consensus on the centrality proof should have in the compulsory school curricula. However, the institutional statements share difficulty to express this objective. The vocabulary includes words such as argument, justification and proof without clear reasons for such diversity: are these words mere synonymous or are there differences that we should pay attention to? What are the characteristics of the discourse these words may refer to in the mathematics classroom? Eventually, how can be addressed the problem of assessing the truth value of a mathematical statement at the different grades all along compulsory school? I shall explore these questions, starting from questioning the meaning of these words and its consequences. Then, I shall shape the relations between argumentation and proof from an epistemological and didactical perspective. In the end, the participants will be invited to a discussion on the benefit and relevance of shaping the notion of mathematical argumentation as a precursor of mathematical proof.
Examine how nature is discussed throughout The Open Boat.” Loo.docxcravennichole326
Examine how nature is discussed throughout “The Open Boat.” Look at the literary critical piece by Anthony Channell Hilfer. Once you have established your own ideas, consider how Hilfer discusses nature in the short story and analyze the following questions: What does nature mean to the men aboard the boat? or Do their perceptions of nature shift throughout the story? Why or why not?
Do their perceptions of nature shift throughout the story? Why or why not?
Write down a loose response about what I think of the question and what I remember of the story.
ICE method.
I introduce the citation
C the citation itself
E explain its meaning to your argument.
The scenes shift with no discernable rhyme or reason. Crane invites every reader in. Critic Anthony Channell Hilfer disagrees with point, saying, “Crane’s image is an accusation of the putative picturesque spectators” (Hilfer 254). Hilfer’s challenge goes against what Crane is trying to do, by making nature a copilot through the reading.
3. Nature as Protagonist in “The Open Boat”
Anthony Channell Hilfer
Texas Studies in Literature and Language, Volume 54, Number 2, Summer
2012, pp. 248-257 (Article)
Published by University of Texas Press
DOI:
For additional information about this article
[ Access provided at 9 Apr 2020 17:36 GMT from Marymount University & (Viva) ]
https://doi.org/10.1353/tsl.2012.0012
https://muse.jhu.edu/article/476402
https://doi.org/10.1353/tsl.2012.0012
https://muse.jhu.edu/article/476402
Anthony Channell Hilfer248
3. Nature as Protagonist in “The Open Boat”
The bottom of the sea is cruel.
—Hart Crane, “Voyages”
As many critics have argued, questions of perspective and epistemology are
central to Stephen Crane’s “The Open Boat” (Kent; Hutchinson). The story’s
first sentence famously clues us to this: “None of them knew the color of
the sky” (68). But behind the uncertainties of perspective is a determinable
ontology, a presence, or rather, I shall argue, a sort of presence, the existence
of which implies a rectified aesthetic response. This response emerges, how-
ever, from negations, denials, and occultations: what is not seen, who is not
there, and what does not happen.3 Here again, when we look at nature we
behold things that are not there and miss “the nothing that is.”
Fully as much as Stevens in “The Snow Man,” Crane is concerned
with certain conventions of representation: personification, the pictur-
esque, the American sublime, and the melodramatic, which although it
does not inform “The Snow Man” is played on in Stevens’s “The Ameri-
can Sublime.” Crane’s story is intertextual with nature poetry, sentimental
poetry, hymns, and landscape art, as well as with Darwinism, theological
clichés, and, less obviously, theological actualities. For the most part these
conventions add up to what the Stevens poem declares is “not there.” To
get to “the nothing that is” we must first traverse this ocean of error. Doing
so helps keep our p.
Examine All Children Can Learn. Then, search the web for effec.docxcravennichole326
Examine
"All Children Can Learn"
. Then, search the web for effective, evidence-based differentiated strategies that are engaging, motivating, and address the needs of individual learners.
First, provide five evidence-based strategies:
Two instructional strategies (i.e., graphic organizers),
Two instructional tools (e.g., technology tool, device or iPad App, Web Quests, etc.),
One activity (e.g., Think-Pair-Share).
Second, for the two instructional strategies you listed explain how you can alter each to address the classroom needs you designed in Weeks One and Two and how the modification is relevant to the theory of differentiation.
.
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Prove asymptotic upper and lower hounds for each of the following sp.pdfwasemanivytreenrco51
Prove asymptotic upper and lower hounds for each of the following specified otherwise, assume
that in each case, T(n) = 1 (or any small constant) for small value You may assume that n = c^k
for some constant c that you choose. Make your bounds as tight as (No need to specify the
origin of your guess.) T(n0 = 8T(n/3) + n^1.83838383... T(n) = T(n - 1) = 1/n T(n) = 16T(n/2)
+ (n log n)^4. T(n) = 2T(n/2) + n/lg n. T(n) = T(n - 1) + T(n - 2) + 1 with base case of T(1) = 1
and T(2) = 2
Solution
A statement are often outlined as a declaratory sentence, or a part of a sentence, that\'s capable of
getting a truth-value, like being true or false. So, as an example, the subsequent area unit
statements:
George W. Bush is that the forty third President of the us.
Paris is that the capital of France.
Everyone born on Monday has purple hair.
Sometimes, a press release will contain one or a lot of alternative statements as elements.
contemplate as an example, the subsequent statement:
Either Ganymede may be a moon of Jupiter or Ganymede may be a moon of Saturn.
While the on top of sentence is itself a press release, as a result of it\'s true, the 2 elements,
\"Ganymede may be a moon of Jupiter\" and \"Ganymede may be a moon of Saturn\", area unit
themselves statements, as a result of the primary is true and therefore the second is fake.
The term proposition is typically used synonymously with statement. However, it\'s typically
accustomed name one thing abstract that 2 totally different statements with an equivalent which
means area unit each aforementioned to \"express\". during this usage, nation sentence, \"It is
raining\", and therefore the French sentence \"Il pleut\", would be thought-about to specific an
equivalent proposition; equally, the 2 English sentences, \"Callisto orbits Jupiter\" and \"Jupiter
is orbitted by Callisto\" would even be thought-about to specific an equivalent proposition.
However, the character or existence of propositions as abstract meanings continues to be a matter
of philosophical dispute, and for the needs of this text, the phrases \"statement\" and
\"proposition\" area unit used interchangeably.
Propositional logic, conjointly referred to as linguistic string logic, is that branch of logic that
studies ways that of mixing or neutering statements or propositions to create a lot of difficult
statements or propositions. change of integrity 2 easier propositions with the word \"and\" is one
common approach of mixing statements. once 2 statements area unit joined along side \"and\",
the advanced statement fashioned by them is true if and as long as each the element statements
area unit true. owing to this, associate argument of the subsequent kind is logically valid:
Paris is that the capital of France and Paris contains a population of over 2 million.
Therefore, Paris contains a population of over 2 million.
Propositional logic for the most part involves learning logical connectives like the words \"and\"
and \"or\" and therefo.
This document provides an overview of logic, proofs, and their applications. It begins with definitions of logic and logical operations like conjunction, disjunction, and negation. It then discusses different types of proofs like direct proofs, proof by contradiction, and proof by induction. Examples are provided to illustrate logical operations and different proof techniques. The document concludes by discussing two applications of logic and proofs - translating English sentences into logical statements and performing Boolean searches.
This document provides an overview of logic and proofs. It begins by defining logic as the study of correct reasoning, and discusses how logic is used in mathematics and computer science. Some key concepts introduced include:
- Propositions and truth values
- Logical connectives like AND, OR, NOT
- Truth tables for evaluating compound propositions
- Quantifiers like "for all" and "there exists"
- Propositional functions and their domains
- Types of proofs like direct proof, proof by contradiction, and mathematical induction
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There are also sub-topics in this presentation like logical connective, atomic sentence, complex sentence, and quantifiers.
This PPT is very helpful for Computer science and Computer Engineer
(B.C.A., M.C.A., B.TECH. , M.TECH.)
Discrete Mathematics covers fundamentals of logic including propositions, truth tables, logical connectives, and propositional equivalences. A proposition is a statement that is either true or false. Logical connectives such as "and", "or", "not" are used to combine propositions into compound statements. Truth tables are used to determine the truth value of compound propositions based on the truth values of the individual propositions. Logical equivalences show that two statements are logically equivalent even if written differently. Examples help illustrate key concepts such as tautologies, contradictions and using equivalences to prove statements.
This document presents an overview of Rossella Marrano's talk on a qualitative perspective on vagueness and degrees of truth. The talk explores representing vagueness through comparative judgments of truth between sentences, rather than precise numerical assignments. It proposes axioms for a binary relation between sentences based on one being "more true" than the other. Representation results show that real-valued truth functions can arise from satisfying the axioms. The approach aims to address objections that assigning precise numerical truth values replaces vagueness with artificial precision.
The document provides an introduction to formal logic. It discusses how to formulate valid arguments through propositional logic and syllogistic logic. Propositional logic uses truth tables to evaluate combinations of propositions and operators like negation and conjunction. Syllogistic logic examines implications of general statements using domains and categories. The key rules of inference for valid arguments are hypothetical syllogism, modus ponens, and modus tollens.
The document discusses deductive and inductive arguments. It provides examples of valid and invalid deductive arguments using categorical propositions and conditional premises. It also discusses inductive arguments, noting that inductive conclusions generalize from specific premises rather than necessarily following from them. The document then compares deductive and inductive arguments and discusses their uses in everyday life and mathematics. It concludes by introducing some common rules of inference for deductive arguments.
This document provides an overview of logic and proofs in discrete mathematics. It discusses topics such as:
- Propositions and truth tables
- Logical connectives like conjunction, disjunction, negation, implication, and equivalence
- Quantifiers like universal and existential
- Different types of proofs like direct proof, proof by contradiction, and mathematical induction
- Rules of inference for propositional and quantified logic
- Resolution proofs
The document serves as an introduction to fundamental concepts in logic that are important for mathematical reasoning and proof techniques.
The document provides an introduction to discrete structures and mathematical reasoning. It discusses key concepts like propositions, logical operators, quantification, and proof techniques. Propositions can be combined using logical operators like negation, conjunction, disjunction, etc. Quantifiers like universal and existential are used to represent statements about all or some elements. Mathematical reasoning involves using axioms, rules of inference, and deductive proofs to establish theorems from given conditions.
Mathematical argumentation as a precursor of mathematical proofNicolas Balacheff
Along history or across educational traditions, the space given to mathematical proof in compulsory school curricula varies from a quasi-absence to a formal obligation which for some has turned into an obstacle to mathematics learning. The contemporary evolution is to give to proof the space it deserves in the learning of mathematics. This is for example witnessed in different ways by The national curriculum in England (2014), the Common Core State Standards for Mathematics (2010) in the US or the recent Report on the teaching of mathematics (1918) commissioned by the French government; the latter asserts: The notion of proof is at the heart of mathematical activity, whatever the level (this assertion is valid from kindergarten to university). And, beyond mathematical theory, understanding what is a reasoned justification approach based on logic is an important aspect of citizen training. The seeds of this fundamentally mathematical approach are sown in the early grades. These are a few examples of the current worldwide consensus on the centrality proof should have in the compulsory school curricula. However, the institutional statements share difficulty to express this objective. The vocabulary includes words such as argument, justification and proof without clear reasons for such diversity: are these words mere synonymous or are there differences that we should pay attention to? What are the characteristics of the discourse these words may refer to in the mathematics classroom? Eventually, how can be addressed the problem of assessing the truth value of a mathematical statement at the different grades all along compulsory school? I shall explore these questions, starting from questioning the meaning of these words and its consequences. Then, I shall shape the relations between argumentation and proof from an epistemological and didactical perspective. In the end, the participants will be invited to a discussion on the benefit and relevance of shaping the notion of mathematical argumentation as a precursor of mathematical proof.
Similar to Chapter 1 Logic and ProofPropositional Logic SemanticsPropo.docx (20)
Examine how nature is discussed throughout The Open Boat.” Loo.docxcravennichole326
Examine how nature is discussed throughout “The Open Boat.” Look at the literary critical piece by Anthony Channell Hilfer. Once you have established your own ideas, consider how Hilfer discusses nature in the short story and analyze the following questions: What does nature mean to the men aboard the boat? or Do their perceptions of nature shift throughout the story? Why or why not?
Do their perceptions of nature shift throughout the story? Why or why not?
Write down a loose response about what I think of the question and what I remember of the story.
ICE method.
I introduce the citation
C the citation itself
E explain its meaning to your argument.
The scenes shift with no discernable rhyme or reason. Crane invites every reader in. Critic Anthony Channell Hilfer disagrees with point, saying, “Crane’s image is an accusation of the putative picturesque spectators” (Hilfer 254). Hilfer’s challenge goes against what Crane is trying to do, by making nature a copilot through the reading.
3. Nature as Protagonist in “The Open Boat”
Anthony Channell Hilfer
Texas Studies in Literature and Language, Volume 54, Number 2, Summer
2012, pp. 248-257 (Article)
Published by University of Texas Press
DOI:
For additional information about this article
[ Access provided at 9 Apr 2020 17:36 GMT from Marymount University & (Viva) ]
https://doi.org/10.1353/tsl.2012.0012
https://muse.jhu.edu/article/476402
https://doi.org/10.1353/tsl.2012.0012
https://muse.jhu.edu/article/476402
Anthony Channell Hilfer248
3. Nature as Protagonist in “The Open Boat”
The bottom of the sea is cruel.
—Hart Crane, “Voyages”
As many critics have argued, questions of perspective and epistemology are
central to Stephen Crane’s “The Open Boat” (Kent; Hutchinson). The story’s
first sentence famously clues us to this: “None of them knew the color of
the sky” (68). But behind the uncertainties of perspective is a determinable
ontology, a presence, or rather, I shall argue, a sort of presence, the existence
of which implies a rectified aesthetic response. This response emerges, how-
ever, from negations, denials, and occultations: what is not seen, who is not
there, and what does not happen.3 Here again, when we look at nature we
behold things that are not there and miss “the nothing that is.”
Fully as much as Stevens in “The Snow Man,” Crane is concerned
with certain conventions of representation: personification, the pictur-
esque, the American sublime, and the melodramatic, which although it
does not inform “The Snow Man” is played on in Stevens’s “The Ameri-
can Sublime.” Crane’s story is intertextual with nature poetry, sentimental
poetry, hymns, and landscape art, as well as with Darwinism, theological
clichés, and, less obviously, theological actualities. For the most part these
conventions add up to what the Stevens poem declares is “not there.” To
get to “the nothing that is” we must first traverse this ocean of error. Doing
so helps keep our p.
Examine All Children Can Learn. Then, search the web for effec.docxcravennichole326
Examine
"All Children Can Learn"
. Then, search the web for effective, evidence-based differentiated strategies that are engaging, motivating, and address the needs of individual learners.
First, provide five evidence-based strategies:
Two instructional strategies (i.e., graphic organizers),
Two instructional tools (e.g., technology tool, device or iPad App, Web Quests, etc.),
One activity (e.g., Think-Pair-Share).
Second, for the two instructional strategies you listed explain how you can alter each to address the classroom needs you designed in Weeks One and Two and how the modification is relevant to the theory of differentiation.
.
Examine each of these items, which are available on the internet .docxcravennichole326
Examine each of these items, which are available on the internet:
1) for music, listen to the first movement of J.S. Bach's MAGNIFICAT; this is the High Baroque era. If you can find a performance with Sir John Eliot Gardiner and his Monteverdi Choir and the English Baroque soloists, go for it.
2) For art, find Giovanni Bellini's ST. FRANCIS IN THE DESERT; you might want to read up on the background of this wonderful painting. Not only St. Francis, but what else do you notice i the painting?
3) For architecture, look at the church at Melk Abbey, Austria; BE SURE to look at the interior shots. Again,
this is high Baroque--but in post-Reformation Catholicism, it had a political aim, too; can you figure it out?
After you have analyzed these, telling what you think the artists/musicians valued and were trying to express, tell me what
YOU think about them! Remember, if you read up on these items, LIST THE WORKS YOU CONSULTED! That way, you avoid plagiarism.
write a 1-page paper on each of these three, telling 1) where they found this value, 2) why it was important “back then,” and 3) is it still around today.
.
Examine a web browser interface and describe the various forms .docxcravennichole326
Examine a web browser interface and describe the various forms of analogy and composite interface metaphors that have been used in its design. What familiar knowledge has been combined with new functionality? need a couple of paragraphs.. and one reference
need this in the next 4 hours..
.
Examine a scenario that includes an inter-group conflict. In this sc.docxcravennichole326
Examine a scenario that includes an inter-group conflict. In this scenario, you are recognized as an authority in cross-cultural psychology and asked to serve as a consultant to help resolve the conflict. You will be asked to write up your recommendations in a 6-page paper not including your title and reference page.
Darley, J.M. & Latané, B. (1968). Bystander interview in emergencies: Diffusion of responsibility.
Journal of Personality and Social Psychology, 8
(4), 377-383.
Scenario: Culture, Psychology, and Community
Imagine an international organization has approached you to help resolve an inter-group conflict. You are an authority in cross-cultural psychology and have been asked to serve as a consultant based on a recent violent conflict involving a refugee community in your town and a local community organization. In the days, weeks, and months leading up to the violent conflict, there were incidents of discrimination and debates regarding the different views and practices people held about work, family, schools, and religious practice. Among the controversies has been the role of women’s participation in political, educational, and community groups
.
Part 1: Developing an Understanding
(2 pages)
Based on the scenario, explain how you can help integrate the two diverse communities so that there is increased understanding and appreciation of each group by the other group. (
Note
: Make sure to include in your explanation the different views and practices of cultural groups as well as the role of women.)
Based on your knowledge of culture and psychology, provide three possible suggestions/solutions that will help the community as a whole. In your suggestions make sure to include an explanation regarding group think and individualism vs. collectivism.
Part 2: Socio-Emotional, Cognitive, and Behavioral Aspects
(2 pages)
Based on your explanations in Part 1, how do your suggestions/solutions impact the socio-emotional, cognitive, and behavior aspects of the scenario and why?
Part 3: Gender, Cultural Values and Dimensions, and Group Dynamics
(2 pages)
Explain the impact of gender, cultural values and dimensions, and group dynamics in the scenario.
Further explain any implications that may arise from when working between and within groups.
Support your Assignment by citing all resources in APA style, including those in the Learning Resources.
.
Examine a current law, or a bill proposing a law, that has to do wit.docxcravennichole326
Examine a current law, or a bill proposing a law, that has to do with technology and criminal activity. The law can be at the state or federal level. Identify the law or bill, where it comes from, and its purpose or intent. Next, identify positive outcomes if the law is successful. Finally, identify at least two unintended consequences that the law could bring about. . . DUE 4/18, 2021
.
Exam IT 505Multiple Choice (20 questions , 2 points each)Pleas.docxcravennichole326
Exam IT 505
Multiple Choice (20 questions , 2 points each)
Please Submit a word document of your exam. Please DO NOT repeat the questions. Only submit your answers for example 1.A, 2. B……Ect
1. Which of the following is NOT one of the typical characteristics of back-end networks?
A. high data rate B. high-speed interface
C. distributed access D. extended distance
2. Problems with using a single Local Area Network (LAN) to interconnect devices
on a premise include:
A. insufficient reliability, limited capacity, and inappropriate network
interconnection devices
B. insufficient reliability, limited capacity, and limited distances
C. insufficient reliability, limited distances, and inappropriate network
interconnection devices
D. limited distances, limited capacity, and inappropriate network
interconnection devices
3. Which of following is NOT one of the designs that determines data rate and
distance?
A. the number of senders B. the number of receivers
C. transmission impairment D. bandwidth
4. The fact that signal strength falls off with distance is called ________________.
A. bandwidth B. attenuation
C. resistance D. propagation
5. Which of the following is NOT one of the distinguishing characteristics for optical
fiber cables compared with twisted pair or coaxial cables?
A. greater capacity B. lower attenuation
C. electromagnetic isolation D. heavier weight
6.________ is a set of function and call programs that allow clients and servers to intercommunicate.
A. IaaS B. SQL C. API D. Middleware
7. A computer that houses information for manipulation by networked clients is a __________.
A. server B. minicomputer C. PaaS D. broker
8. ________ is software that improves connectivity between a client application and a server.
A. SQL B. API C. Middleware D. SAP
9. The inability of frame relay to do hop by hop error control is offset by:
A. its gigabit speeds B. its high overhead
C. the extensive use of in-band signaling D. the increasing reliability of networks
10. All Frame Relay nodes contain which of the following protocols?
A. LAPB B. LAPD
C. LAPF Core D. LAPF Control
11. The technique employed by Frame Relay is called __________.
A. inband signaling B. outband signaling
C. common channel signaling D. open shortest path first routing
12. In ATM, the basic transmission unit is the ________.
A. frame B. cell
C. packet D. segment
13. When using ATM, which of the following is NOT one of the advantages for the
use of virtual paths?
A. less work is needed to set a virtual path
B. the network architecture is simplified
C.
EXAM
Estructura 8.1 - Miniprueba A
Verbos
Complete the chart with the correct verb forms.
infinitivo
seguir
(1) [removed]
yo
(2) [removed]
morí
tú
seguiste
(3) [removed]
nosotras
seguimos
(4) [removed]
ellos
(5) [removed]
murieron
Completar
Fill in the blanks with the correct preterite forms of the verbs in parentheses.
Diego y Javier [removed] (conseguir) un mapa.
Esta mañana usted [removed] (despedirse) de los estudiantes.
Tú [removed] (sentirse) mal ayer.
La semana pasada yo no [removed] (dormir) bien.
Amparo [removed] (preferir) comer en casa.
Oraciones
Write sentences using the information provided. Use the preterite and make any necessary changes.
Modelo
Edgar / preferir / pollo asado
Edgar prefirió el pollo asado.
Álvaro y yo / servir / los entremeses
[removed]
¿quién / repetir / las instrucciones?
[removed]
ayer / yo / despedirse / de / mis sobrinos
[removed]
ustedes / dormirse / a las diez
[removed]
La cena
Fill in the blanks with the preterite form of the appropriate verbs from the list. Four verbs will not be used.
abrir
conseguir
escoger
leer
mirar
pedir
preferir
probar
repetir
sentirse
servir
vestirse
Anoche Jorge, Iván y yo salimos a cenar a Mi Tierra, un restaurante guatemalteco. Nosotros
(1) [removed]
este lugar porque Jorge
(2) [removed]
una reseña (
review
) en Internet que decía (
said
) que la comida es auténtica y muy sabrosa. No es un restaurante elegante; entonces nosotros
(3) [removed]
de bluejeans. De verdad, en Mi Tierra mis amigos y yo
(4) [removed]
como (
like
) en casa. El camarero que nos
(5) [removed]
fue muy amable. Para empezar, Jorge e Iván
(6) [removed]
tamales, pero yo
(7) [removed]
esperar el plato principal: carne de res con arroz y frijoles. Comimos tanto (
so much
) que no
(8) [removed]
nada de postre (
dessert
). ¡Fue una cena deliciosa!
.
Examine current practice guidelines related to suicide screeni.docxcravennichole326
Examine current practice guidelines related to suicide screening and prevention and how they could pertain to John.
Choose two of the following questions to answer as part of your initial post.
What events in John's life created a "downward spiral" into homelessness and hopelessness? Which events were related to social needs, mental health needs, and medical needs, and which could health care have addressed?
What were some of the barriers John faced in accessing medical care and mental health care?
How does homelessness and mental illness intersect? Do you believe homelessness may develop because of a mental health issue, or do you believe those who become homeless eventually sink into psychological despair?
The tipping point for many people who live at the margins of society may be things that could have been managed given the right support. How can your role as an APRN help identify, alleviate, or support those who are in need like John?
In your own experience, have you encountered a homeless individual? What was that like? Do you recall what you were thinking?
Please include at least three scholarly sources within your initial post.
Rubric:
Discussion Question Rubric
Note:
Scholarly resources are defined as evidence-based practice, peer-reviewed journals; textbook (do not rely solely on your textbook as a reference); and National Standard Guidelines. Review assignment instructions, as this will provide any additional requirements that are not specifically listed on the rubric.
Discussion Question Rubric – 100 PointsCriteriaExemplary
Exceeds ExpectationsAdvanced
Meets ExpectationsIntermediate
Needs ImprovementNovice
InadequateTotal PointsQuality of Initial PostProvides clear examples supported by course content and references.
Cites three or more references, using at least one new scholarly resource that was not provided in the course materials.
All instruction requirements noted.
40 points
Components are accurate and thoroughly represented, with explanations and application of knowledge to include evidence-based practice, ethics, theory, and/or role. Synthesizes course content using course materials and scholarly resources to support importantpoints.
Meets all requirements within the discussion instructions.
Cites two references.
35 points
Components are accurate and mostly represented primarily with definitions and summarization. Ideas may be overstated, with minimal contribution to the subject matter. Minimal application to evidence-based practice, theory, or role development. Synthesis of course content is present but missing depth and/or development.
Is missing one component/requirement of the discussion instructions.
Cites one reference, or references do not clearly support content.
Most instruction requirements are noted.
31 points
Absent application to evidence-based practice, theory, or role development. Synthesis of course content is superficial.
Demonstrates incomplete understandin.
Examine Case Study Pakistani Woman with Delusional Thought Processe.docxcravennichole326
Examine Case Study: Pakistani Woman with Delusional Thought Processes.
You will be asked to make three decisions concerning the medication to prescribe to this client. Be sure to consider factors that might impact the client’s pharmacokinetic and pharmacodynamic processes.
At each decision point stop to complete the following:
Decision #1
Which decision did you select?
Why did you select this decision? Support your response with evidence and references to the Learning Resources.
What were you hoping to achieve by making this decision? Support your response with evidence and references to the Learning Resources.
Explain any difference between what you expected to achieve with Decision #1 and the results of the decision. Why were they different?
Decision #2
Why did you select this decision? Support your response with evidence and references to the Learning Resources.
What were you hoping to achieve by making this decision? Support your response with evidence and references to the Learning Resources.
Explain any difference between what you expected to achieve with Decision #2 and the results of the decision. Why were they different?
Decision #3
Why did you select this decision? Support your response with evidence and references to the Learning Resources.
What were you hoping to achieve by making this decision? Support your response with evidence and references to the Learning Resources.
Explain any difference between what you expected to achieve with Decision #3 and the results of the decision. Why were they different?
Also include how ethical considerations might impact your treatment plan and communication with clients.
BACKGROUND
The client is a 34-year-old Pakistani female who moved to the United States in her late teens/early 20s. She is currently in an “arranged” marriage (her husband was selected for her since she was 9 years old). She presents to your office today following a 21 day hospitalization for what was diagnosed as “brief psychotic disorder.” She was given this diagnosis as her symptoms have persisted for less than 1 month.
Prior to admission, she was reporting visions of Allah, and over the course of a week, she believed that she was the prophet Mohammad. She believed that she would deliver the world from sin. Her husband became concerned about her behavior to the point that he was afraid of leaving their 4 children with her. One evening, she was “out of control” which resulted in his calling the police and her subsequent admission to an inpatient psych unit.
During today’s assessment, she appears quite calm, and insists that the entire incident was “blown out of proportion.” She denies that she believed herself to be the prophet Mohammad and states that her husband was just out to get her because he never loved her and wanted an “American wife” instead of her. She tells you that she knows this because the television is telling her so.
She currently weighs .
Examination of Modern LeadershipModule 1 Leadership History, F.docxcravennichole326
Examination of Modern Leadership
Module 1: Leadership: History, Fundamentals, and the Modern Context
Module 1 content establishes the context for the entire course dedicated to the examination of modern and postmodern leadership. The introduction of critical theory and its use in ORG561 provides a framework for investigation. The context of social, economic, political, and technological environments informs an exploration of modern and postmodern leadership approaches. Emphasis on leader self-awareness sets the stage for reflection, introspection, and personal leadership development.
Learning Outcomes
1. Compare and contrast historical leadership concepts against modern and postmodern organization needs.
2. Analyze leadership approaches using a critical framework.
3. Construct a personal leadership biography.
For Your Success & Readings
A key to success in ORG561 is to start early, build, reflect, reinforce, build, reflect, and reinforce.
Begin each week’s study by reading and comprehending the learning outcomes. Learning outcomes are always revealed in assignments, discussions, and lectures. Likewise, learning outcomes are reflected in rubrics, which are used as objective measures for scoring and grading. Establish the learning outcomes as your checklist for success.
In Module 1 criticaltheory is introduced through the readings, lecture, discussion, and Critical Thinking Assignment. The critical approach provides new frameworks on which to research leadership. You may not be familiar with critical inquiry, so seize the opportunity to advance your analytic skills. You are expected to use one or more critical frames in each module of this course. Take the time this week to fully understand the reasoning and context of critical theory.
Studying the history of leadership requires reading publications from earlier eras. Notice that some of the required and recommended readings for Module 1 are not current publications, but these contribute to understanding the earlier periods of organization and leadership study.
Postmodern leadership literature expounds on the notion that self-awareness is a critical component required to lead. In ORG561, the thread of self-examination is woven throughout the course. You will have opportunities to move beyond reflection to develop a better understanding of personal assumptions and biases, skills and competencies, and professional development plans, all related to leadership. Embrace the opportunity!
Required
· Introduction and Chapters 1 & 2 in Leadership: A Critical Text
· Axley, S. R. (1990). The practical qualities of effective leaders. Industrial Management, 32(5), 29-31.
· Brocato, B., Jelen, J., Schmidt, T., & Gold, S. (2011). Leadership conceptual ambiguities.Journal of Leadership Studies, 5(1), 35-50. doi:10.1002/jls.20203
· Gandolfi, F., & Stone, S. (2016). Clarifying leadership: High-impact leaders in a time of leadership crisis. Revista De Management Comparat International, 17(3), 212-224.
· Blom, M. .
Examine current international OB issues that challenge organizat.docxcravennichole326
Examine current international OB issues that challenge organizational leaders to resolve critical issues involving cross-cultural communication, negotiation, leadership, motivation, decision-making, among others.
(1) identify the key organizational behavior issues facing management,
(2) what impact the international environment has on these issues,
(3) strategies management should use to overcome these issues,
(4) how these strategies will impact the overall organizational operations, and
(5) identify the potential costs and risks to the organizations of implementing the newly developed strategies.
Offer a set of recommendations, which must be derived from both data and theory. Teams must include aspects of global leadership, global motivation and global team-management in their work.
APA format, Times New Roman (12), 20-25 pages, No plagiarism.
.
Executive Program Practical Connection Assignment .docxcravennichole326
Executive Program Practical Connection Assignment
Component Proficient (15 to 20 points) Competent (8 to 14 points) Novice (1 to 7 points) Score
Assignment
Requirements
Student completed all required
portions of the assignment
Completed portions of the
assignment
Did not complete the required
assignment.
Writing Skills,
Grammar, and APA
Formatting
Assignment strongly demonstrates
graduate-level proficiency in
organization, grammar, and style.
Assignment is well written, and ideas
are well developed and explained.
Demonstrates strong writing skills.
Student paid close attention to spelling
and punctuation. Sentences and
paragraphs are grammatically correct.
Proper use of APA formatting. Properly
and explicitly cited outside resources.
Reference list matches citations.
Assignment demonstrates graduate-
level proficiency in organization,
grammar, and style.
Assignment is effectively
communicated, but some sections
lacking clarity. Student paid some
attention to spelling and
punctuation, but there are errors
within the writing. Needs attention
to proper writing skills.
Use of APA formatting and citations
of outside resources, but has a few
instances in which proper citations
are missing.
Assignment does not demonstrate
graduate-level proficiency in
organization, grammar, and style.
Assignment is poorly written and
confusing. Ideas are not
communicated effectively. Student
paid no attention to spelling and
punctuation. Demonstrates poor
writing skills.
The assignment lacks the use of APA
formatting and does not provide
proper citations or includes no
citations.
Maintains
purpose/focus
Submission is well organized and has a
tight and cohesive focus that is
integrated throughout the document
Submissions has an organizational
structure and the focus is clear
throughout.
Submission lacks focus or contains
major drifts in focus
Understanding of
Course Content
Student demonstrates understand of
course content and knowledge.
Student demonstrates some
understanding of course content
and knowledge.
Student does not demonstrate
understanding of course content and
knowledge.
Work Environment
Application
Student strongly demonstrates the
practical application, or ability to apply,
of course objectives within a work
environment.
Student demonstrates some
practical application, or ability to
apply, of course objectives within a
work environment.
Student does not demonstrate the
practical application, or ability to
apply, of course objectives within a
work environment.
Executive Program Practical Connection Assignment
At UC, it is a priority that students are provided with strong educational programs and courses that
allow them to be servant-leaders in their disciplines and communities, linking research with practice and
kn.
Executive Program Practical Connection Assignment Component .docxcravennichole326
Executive Program Practical Connection Assignment
Component
Proficient (15 to 20 points)
Competent (8 to 14 points)
Novice (1 to 7 points)
Score
Assignment Requirements
Student completed all required portions of the assignment
Completed portions of the assignment
Did not complete the required assignment.
Writing Skills, Grammar, and APA Formatting
Assignment strongly demonstrates graduate-level proficiency in organization, grammar, and style.
Assignment is well written, and ideas are well developed and explained. Demonstrates strong writing skills. Student paid close attention to spelling and punctuation. Sentences and paragraphs are grammatically correct.
Proper use of APA formatting. Properly and explicitly cited outside resources. Reference list matches citations.
Assignment demonstrates graduate-level proficiency in organization, grammar, and style.
Assignment is effectively communicated, but some sections lacking clarity. Student paid some attention to spelling and punctuation, but there are errors within the writing. Needs attention to proper writing skills.
Use of APA formatting and citations of outside resources, but has a few instances in which proper citations are missing.
Assignment does not demonstrate graduate-level proficiency in organization, grammar, and style.
Assignment is poorly written and confusing. Ideas are not communicated effectively. Student paid no attention to spelling and punctuation. Demonstrates poor writing skills.
The assignment lacks the use of APA formatting and does not provide proper citations or includes no citations.
Maintains purpose/focus
Submission is well organized and has a tight and cohesive focus that is integrated throughout the document
Submissions has an organizational structure and the focus is clear throughout.
Submission lacks focus or contains major drifts in focus
Understanding of Course Content
Student demonstrates understand of course content and knowledge.
Student demonstrates some understanding of course content and knowledge.
Student does not demonstrate understanding of course content and knowledge.
Work Environment Application
Student strongly demonstrates the practical application, or ability to apply, of course objectives within a work environment.
Student demonstrates some practical application, or ability to apply, of course objectives within a work environment.
Student does not demonstrate the practical application, or ability to apply, of course objectives within a work environment.
.
Executive Program Group Project Assignment Component Profi.docxcravennichole326
Executive Program Group Project Assignment
Component
Proficient (15 to 20 points)
Competent (8 to 14 points)
Novice (1 to 7 points)
Score
Assignment Requirements
Student completed all required portions of the assignment
Completed portions of the assignment
Did not complete the required assignment.
Writing Skills, Grammar, and APA Formatting
Assignment strongly demonstrates graduate-level proficiency in organization, grammar, and style.
Assignment is well written, and ideas are well developed and explained. Demonstrates strong writing skills. Student paid close attention to spelling and punctuation. Sentences and paragraphs are grammatically correct.
Proper use of APA formatting. Properly and explicitly cited outside resources. Reference list matches citations.
Assignment demonstrates graduate-level proficiency in organization, grammar, and style.
Assignment is effectively communicated, but some sections lacking clarity. Student paid some attention to spelling and punctuation, but there are errors within the writing. Needs attention to proper writing skills.
Use of APA formatting and citations of outside resources, but has a few instances in which proper citations are missing.
Assignment does not demonstrate graduate-level proficiency in organization, grammar, and style.
Assignment is poorly written and confusing. Ideas are not communicated effectively. Student paid no attention to spelling and punctuation. Demonstrates poor writing skills.
The assignment lacks the use of APA formatting and does not provide proper citations or includes no citations.
Maintains purpose/focus
Submission is well organized and has a tight and cohesive focus that is integrated throughout the document
Submissions has an organizational structure and the focus is clear throughout.
Submission lacks focus or contains major drifts in focus
Understanding of Course Content
Student demonstrates understand of course content and knowledge.
Student demonstrates some understanding of course content and knowledge.
Student does not demonstrate understanding of course content and knowledge.
Work Environment Application
Student strongly demonstrates the practical application, or ability to apply, of course objectives within a work environment.
Student demonstrates some practical application, or ability to apply, of course objectives within a work environment.
Student does not demonstrate the practical application, or ability to apply, of course objectives within a work environment.
Criteria Excellent Satisfactory Less than Satisfactory Not Completed
Log
Completion
4 points
Food logs are
complete with detailed
food/beverage items
3 points
Food logs are
complete but lack
some detail on
food/beverage items
(3 pts)
2 points
Food logs are
complete are missing
substantial detail on
food/beverage items
0 points
Student did not
complete this
component of the
project.
/ 4
Por.
Executive Practical Connection Activityit is a priority that stu.docxcravennichole326
Executive Practical Connection Activity
it is a priority that students are provided with strong educational programs and courses that allow them to be servant-leaders in their disciplines and communities, linking research with practice and knowledge with ethical decision-making. This assignment is a written assignment where students will demonstrate how this course research has connected and put into practice within their own career.
Assignment:
Provide a reflection of at least 500 words (or 2 pages double spaced) of how the knowledge, skills, or theories of this course have been applied, or could be applied, in a practical manner to your current work environment. If you are not currently working, share times when you have or could observe these theories and knowledge could be applied to an employment opportunity in your field of study.
Requirements:
· Provide a 500 word (or 2 pages double spaced) minimum reflection.
· Use of proper APA formatting and citations. If supporting evidence from outside resources is used those must be properly cited.
· Share a personal connection that identifies specific knowledge and theories from this course.
· Demonstrate a connection to your current work environment. If you are not employed, demonstrate a connection to your desired work environment.
· You should NOT, provide an overview of the assignments assigned in the course. The assignment asks that you reflect how the knowledge and skills obtained through meeting course objectives were applied or could be applied in the workplace.
MY ROLE: BIGDATA/KAFKA ADMIN
Need Plagiarism report for this Assignement.
****Directions
Choose from one of the following tweets and answer the 4 questions, Include at least one scholarly source***** The link is included in each tweet for more information.
1. Identify a healthcare issue within your community and explain the issue to your class colleagues. (You may use the same issue you identified in Week 2, but please expand your responses to address this week's focus).
2. Describe the type of healthcare policy you would advocate for in an effort to change this issue.
3. What type of campaign would you need to launch in order to gather a network of support?
4. Compose a Tweet that describes what you have shared with your class colleagues. Remember, Twitter only allows for 140 characters so you will need to be concise.
1. NR708HealthPol Retweeted
Tara Heagele, PhD, RN, PCCN, EMT@TaraHeagele
#NurseTwitter Hurricane season starts today! Helping Vulnerable People Before Disasters Strike | Campaign for Action https://campaignforaction.org/helping-vulnerable-people-before-disasters-strike/#.XtUB00-UAZ4.twitter …
Helping Vulnerable People Before Disasters Strike | Campaign for Action
Floods, tornadoes, heat waves, blizzards, earthquakes, and hurricanes threaten the health and well-being of millions of people each year
campaignforaction.org
13h
·
·
2. NR708HealthPol Retweeted
Diana Mason@djmasonrn
By @AmyAnderso.
Executive FunctionThe Search for an Integrated AccountMari.docxcravennichole326
Executive Function
The Search for an Integrated Account
Marie T. Banich
Department of Psychology & Neuroscience, and Institute of Cognitive Science, University of Colorado at Boulder;
Department of Psychiatry, University of Colorado Denver
ABSTRACT—In general, executive function can be thought
of as the set of abilities required to effortfully guide be-
havior toward a goal, especially in nonroutine situations.
Psychologists are interested in expanding the under-
standing of executive function because it is thought to be a
key process in intelligent behavior, it is compromised in a
variety of psychiatric and neurological disorders, it varies
across the life span, and it affects performance in compli-
cated environments, such as the cockpits of advanced
aircraft. This article provides a brief introduction to the
concept of executive function and discusses how it is
assessed and the conditions under which it is compromised.
A short overview of the diverse theoretical viewpoints re-
garding its psychological and biological underpinnings is
also provided. The article concludes with a consideration
of how a multilevel approach may provide a more inte-
grated account of executive function than has been previ-
ously available.
KEYWORDS—executive function; frontal lobe; prefrontal
cortex; inhibition; task switching; working memory; atten-
tion; top-down control
Like other psychological constructs, such as memory, executive
function is multidimensional. As such, there exists a variety of
models that provide varying viewpoints as to its basic component
processes. Nonetheless, common across most of them is the idea
that executive function is a process used to effortfully guide
behavior toward a goal, especially in nonroutine situations.
Various functions or abilities are thought to fall under the rubric
of executive function. These include prioritizing and sequencing
behavior, inhibiting familiar or stereotyped behaviors, creating
and maintaining an idea of what task or information is most
relevant for current purposes (often referred to as an attentional
or mental set), providing resistance to information that is dis-
tracting or task irrelevant, switching between task goals, uti-
lizing relevant information in support of decision making,
categorizing or otherwise abstracting common elements across
items, and handling novel information or situations. As can be
seen from this list, the functions that fall under the category of
executive function are indeed wide ranging.
ASSESSING EXECUTIVE FUNCTION
The very nature of executive function makes it difficult to
measure in the clinic or the laboratory; it involves an individual
guiding his or her behavior, especially in novel, unstructured,
and nonroutine situations that require some degree of judgment.
In contrast, standard testing situations are structured—partic-
ipants are explicitly told what the task is, given rules for per-
forming the task, and provide.
Executive Compensation and IncentivesMartin J. ConyonEx.docxcravennichole326
Executive Compensation and Incentives
Martin J. Conyon*
Executive Overview
The objective of a properly designed executive compensation package is to attract, retain, and motivate
CEOs and senior management. The standard economic approach for understanding executive pay is the
principal-agent model. This paper documents the changes in executive pay and incentives in U.S. firms
between 1993 and 2003. We consider reasons for these transformations, including agency theory, changes
in the managerial labor markets, shifts in firm strategy, and theories concerning managerial power. We show that
boards and compensation committees have become more independent over time. In addition, we demonstrate
that compensation committees containing affiliated directors do not set greater pay or fewer incentives.
Introduction
E
xecutive compensation is a complex and con-
troversial subject. For many years, academics,
policymakers, and the media have drawn atten-
tion to the high levels of pay awarded to U.S.
chief executive officers (CEOs), questioning
whether they are consistent with shareholder in-
terests.1 Some academics have further argued that
flaws in CEO pay arrangements and deviations
from shareholders’ interests are widespread and
considerable.2 For example, Lucian Bebchuk and
Jesse Fried provide a lucid account of the mana-
gerial power view and accompanying evidence.3
Marianne Bertrand and Sendhil Mullainathan too
provide an analysis of the ‘skimming view’ of CEO
pay.4 In contrast, John Core et al. present an
economic contracting approach to executive pay
and incentives, assessing whether CEOs receive
inefficient pay without performance.5 In this pa-
per, we show what has happened to CEO pay in
the United States. We do not claim to distinguish
between the contracting and managerial power
views of executive pay. Instead, we document the
pattern of executive pay and incentives in the
United States, investigating whether this pattern
is consistent with economic theory.
The Context: Who Sets Executive Pay?
B
efore examining the empirical evidence pre-
sented in this paper, it is important to consider
the pay-setting process and who sets executive
pay. The standard economic theory of executive
compensation is the principal-agent model.6 The
theory maintains that firms seek to design the most
efficient compensation packages possible in order to
attract, retain, and motivate CEOs, executives, and
managers.7 In the agency model, shareholders set
pay. In practice, however, the compensation com-
mittee of the board determines pay on behalf of
shareholders. A principal (shareholder) designs a
contract and makes an offer to an agent (CEO/
manager). Executive compensation ameliorates a
moral hazard problem (i.e., manager opportunism)
arising from low firm ownership. By using stock
options, restricted stock, and long-term contracts,
shareholders motivate the CEO to maximize firm
value. In other words, shareholders try to design
optimal compensation packages .
Executing the StrategyLearning ObjectivesAfter reading.docxcravennichole326
Executing the Strategy
Learning Objectives
After reading this chapter, you should be able to:
• Distinguish good operational plans from weak ones.
• Detail the value of tracking progress on all operational plans.
• Discuss why emergent strategies occur and how they might affect an organization’s
current strategy.
• Implement the ten basic steps of a generic strategic formulation process.
• Manage, improve, and evaluate an existing strategic management process.
Chapter 9
Neil Webb/Ikon Images/Getty Images
spa81202_09_c09.indd 247 1/16/14 10:08 AM
CHAPTER 9Section 9.1 Managing Operational Plans
Implementing a strategy (see Figure 1.1) in the real world is not a leisurely swim across
a calm pond on a sunny day, but rather like crossing from one bank of a raging river to
the other, encountering hidden eddies, fog, driving rain, lightning, and riptides along the
way. While it is not impossible to reach the other bank (the goal), the task often becomes
one of overcoming obstacles and making constant adjustments without losing sight of the
goal. Implementation is like that. Even the most brilliant strategy is worthless if it cannot
be implemented.
This chapter focuses on strategy execution and its difficulties. Part of the chapter is devoted
to assessing, improving, and managing the strategy formulation process itself.
9.1 Managing Operational Plans
The process for obtaining board approval of operational plans is covered in this chapter.
Exactly what is it that gets approved? An operational plan is a document that specifies the
projects or tasks that must be accomplished to achieve particular operational objectives.
Many of these plans will contain activities that are ongoing. Some will include plans for
enhanced or new services. Details specified in operational plans include the names of those
who will be involved and the indi-
vidual responsible for each one, what
equipment will be needed, when each
will start and end, and the estimated
costs for each activity. Given the level
of detail required, it should come as
no surprise that an operational plan
for a large functional unit, such as the
nursing department in a hospital, can
run to many pages, as there are lots of
activities to be detailed. Operational
plans for small HSOs such as physi-
cian clinics and community health
centers may be just a few pages long
unless new strategic initiatives are to
be undertaken.
It takes contributions from everyone
who will be involved in that HSO’s
operations to create such plans. They
will make sure that continuing cur-
rent operations are included in the plans, which is easily done. What adds a level of com-
plexity and difficulty is incorporating additional tasks demanded by a change in strategy.
Consider the following scenarios, which illustrate the difficulty in creating operational
plans that involve more than simply repeating what was done the previous year:
Javier Larrea/age fotostock/Getty Ima.
Executing Strategies in a Global Environment Examining the Case of .docxcravennichole326
Executing Strategies in a Global Environment: Examining the Case of Federal Express 5-7 pages
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How to Setup Warehouse & Location in Odoo 17 InventoryCeline George
In this slide, we'll explore how to set up warehouses and locations in Odoo 17 Inventory. This will help us manage our stock effectively, track inventory levels, and streamline warehouse operations.
This slide is special for master students (MIBS & MIFB) in UUM. Also useful for readers who are interested in the topic of contemporary Islamic banking.
Strategies for Effective Upskilling is a presentation by Chinwendu Peace in a Your Skill Boost Masterclass organisation by the Excellence Foundation for South Sudan on 08th and 09th June 2024 from 1 PM to 3 PM on each day.
Reimagining Your Library Space: How to Increase the Vibes in Your Library No ...Diana Rendina
Librarians are leading the way in creating future-ready citizens – now we need to update our spaces to match. In this session, attendees will get inspiration for transforming their library spaces. You’ll learn how to survey students and patrons, create a focus group, and use design thinking to brainstorm ideas for your space. We’ll discuss budget friendly ways to change your space as well as how to find funding. No matter where you’re at, you’ll find ideas for reimagining your space in this session.
This presentation includes basic of PCOS their pathology and treatment and also Ayurveda correlation of PCOS and Ayurvedic line of treatment mentioned in classics.
A review of the growth of the Israel Genealogy Research Association Database Collection for the last 12 months. Our collection is now passed the 3 million mark and still growing. See which archives have contributed the most. See the different types of records we have, and which years have had records added. You can also see what we have for the future.
How to Manage Your Lost Opportunities in Odoo 17 CRMCeline George
Odoo 17 CRM allows us to track why we lose sales opportunities with "Lost Reasons." This helps analyze our sales process and identify areas for improvement. Here's how to configure lost reasons in Odoo 17 CRM
A workshop hosted by the South African Journal of Science aimed at postgraduate students and early career researchers with little or no experience in writing and publishing journal articles.
South African Journal of Science: Writing with integrity workshop (2024)
Chapter 1 Logic and ProofPropositional Logic SemanticsPropo.docx
1. Chapter 1: Logic and Proof
Propositional Logic Semantics
Propositional variables: p, q, r, s, ... (stand for simple
sentences)
T: any proposition that is always true
F: any proposition that is always false
Compound propositions: formed from propositional variables
and logical operators (all binary except negation):
Negation ¬
Conjunction ∧
Disjunction ∨
Implication →
Biconditional ↔
Exclusive Or ⊕
Truth Tables: assign all possible T, F to all possible variables,
and determines all possible T, F of compound propositions; with
n variables there are 2n rows in the table
Negation changes T to F and vice versa
Conjunction is only T if both conjuncts are T
Disjunction is only F is both disjuncts are F
Implication is only F is the antecedent is T and the consequent
is F
Biconditional is only true if they have the same tvalue
Exclusive Or is only T if they differ in tvalue
Two (compound) propositions are equivalent (≡) iff they always
have the same tvalue (see also below)
English translations:
Conjunction: and, but, although, yet, still, ...
Disjunctions: or, unless
Implication: if, if ... then, only if, when, implies, entails,
follows from, is sufficient, is necessary, when, whenever
Biconditional: if and only if, just in case, is necessary and
sufficient
2. A set of propositions is consistent iff there is some assignment
of tvalue that makes all T
A set of propositions is inconsistent iff there is no assignment
of tvalue that makes all T
A tautology is a compound propositions that is always T
A contradiction is a compound propositions that is always F
A contingency is a compound propositions that is sometimes T,
sometimes F
A compound proposition is satisfiable iff some assignment of
tvalues make it T
A compound proposition is unsatisfiable iff no assignment of
tvalues make it T
Two compound propositions p and q are logically equivalent iff
p ↔ q is a tautology
Common equivalences:
DeMorgan’s Laws (Dem)
¬(p ∨ q)≡¬p ∧ ¬q
¬(p ∧ q)≡¬p ∨ ¬q
Identity Laws (Id)
p ∧ T ≡p
p ∨ F ≡p
Domination Laws (Dom)
p ∨ T ≡T
p ∧ F ≡F
Idempotent Laws (Idem)
p ∨ T ≡T
p ∧ p ≡p
Double Negation Law (DN)
¬(¬p) ≡ p
Negation Laws (Neg)
p ∨ ¬p ≡T
p ∧ ¬p ≡F
Commutative Laws (Comm)
p ∨ q ≡q ∨ p
p ∧ q ≡q ∧ p
3. Associative Laws (Assoc)
(p ∨ q) ∨ r ≡p ∨ (q ∨ r)
(p ∧ q) ∧ r ≡p ∧ (q ∧ r)
Distributive Laws (Dist)
p ∨ (q ∧ r) ≡
(p ∨ q) ∧ (p ∨ r)
p ∧ (q ∨ r) ≡
(p ∧ q) ∨ (p ∧ r)
Absorption Laws (Abs)
p ∨ (p ∧ q) ≡ p
p ∧ (p ∨ q) ≡ p
Conditional Laws (Cond)
p →q≡ ¬p ∨ q
¬(p →q)≡ p ∧ ¬q
Biconditional Law (Bicond)
p ↔ q ≡ (p →q) ∧ (q →p)
Quantifier Negation (QNeg)
¬ ∀ x P ( x ) ≡ ∃ x ¬ P ( x )
¬ ∃ x P ( x ) ≡ ∀ x ¬ P ( x )
Predicate and Relational Logic (Quantificational Logic, First
Order Logic): Semantics
Variables: x, y, z, ...
Predicates/Relations, Propositional Functions: P(x), M(x),
Q(x,y), S(x,y,z), ...
Constants: a, b, c, 0, -1, 4, Socrates, ...
Domain (U): set of things the variables range over
Propositional functions are neither T nor F; however, if all the
variables are replaced by constants they become propositions
and therefore T or F
Universal Quantifier, “For all x”, symbol: x
Existential Quantifier, “There exists an x”, “For some x”,
symbol: x
Some Quantifier Equivalences (DeMorgan’s):
4. An assertion involving predicates and quantifiers is valid iff it
is true: 1) for all domains, and 2) for all propositional functions
An assertion involving predicates and quantifiers is satisfiable
iff it is true: 1) for some domains, and 2) for some propositional
functions
Proofs: Syntactic Rules
An argument is valid iff it has a valid argument form
An argument form is valid iff it is impossible for the premises
to be true and the conclusion false
A argument form isinvalid iff it IS possible for the premises to
be true and the conclusion false (a counterexample exists)
Inferences rules are simple valid argument forms that can be
used to construct more complex arguments.
Each propositional inference rule has associated with it a
tautology: the conjunction of the premises implies the
conclusion
Modus Ponens (MP)
Modus Tollens (MT)
Hypothetical Syllogism (Hyp)
Disjunctive Syllogism (Disj)
Addition (Add)
Simplification (Simp)
Conjunction (Conj)
5. Resolution (Res)
Universal Instantiation (UI – unrestricted)
Universal Generalization (UG – restricted: c must be new to the
proof)
Existential Instantiation (EI – restricted: c must be new to the
proof)
Existential Generalization (EI – unrestricted)
Proofs
Many proofs involve conditionals: to prove if p, then q, assume
p is true and deduce q using the above rules.
A theoremis shown to be true by using: 1) definitions, 2) other
theorems, 3) axioms (which are assumed to be true), and 4) the
rules of inference.
A lemma is an intermediate theorem proven to aid tin the proof
of the final theorem.
A corollaryis a theorem that follows quickly from a theorem.
A conjecture is a non-theorem that one thinks is true.
A direct proof uses the 4 tools used for proving theorems.
An indirect proof is:
A proof that proves the contrapositive instead, or
A proof by contradiction, which assumes the negation of that to
be proved and deduces a contradiction
Disproof by counterexample shows the invalidity of an
argument by finding a domain that makes all of the premises
6. true and makes the conclusion (conjecture) false.
Existence proofs prove the existence of an entity with a certain
property (usually mathematical)
Uniqueness proofs prove BOTH the existence and uniqueness of
an entity with a certain property (usually mathematical): show if
there are two with the property, then they are really the same
(i.e., suppose there are 2, x and y, and show x=y)
Number Theory
n is an even integer iff there exists an integer k, k ≠ 0, and n=2k
n is an odd integer iff there exists an integer k, such that
n=2k+1 or n = 2k-1
4
Why we are looking at the ‘value’ of college all wrong
By Valerie Strauss November 1, 2014
St. John’s College in Annapolis. (Photo by Mark Gail/The
Washington Post)
There is a national debate about whether going to college is
worth the increasingly hefty price tag. The argument against it
is that many students come out four — or five or six — years
later and can’t find a job that pays a lot, or they can’t find a job
at all. But in this post, St. John’s College President Christopher
B. Nelson argues that “education and economics are essentially
incompatible” and that the economic lens is the wrong way to
judge education. Nelson has been president of St. John’s, in
Annapolis, Maryland, since June 1991. Before that he, practiced
law in Chicago for 18 years and was chairman of his law firm.
As university president, he has become a national spokesman
for the liberal arts. St. John’s, with a campus in Annapolis and
7. in Santa Fe, N.M., has an unusual liberal arts curriculum, one
based on discussion of works from the Western Canon.
By Christopher B. Nelson
As college admission deadlines loom, new lists and rankings
proliferate along with reports questioning the “value” of a
college education. The obsession with quantification is rooted
in a habit of applying economic categories to everything. Yet
education and economics are essentially incompatible. The lens
of economics distorts our judgment about the true worth of
higher education.
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The incompatibility rests on a fundamental difference between
economics and education. Begin with the idea of economics as
the science of scarcity. The price of a commodity is largely
dependent on its relative scarcity. Economic value increases
when a commodity becomes scarce, and a commodity that is not
scarce will become scarce if it is distributed widely and used up
indiscriminately. Scarcity is basic to the world view of
economics—so much so that the language of economics speaks
as though scarcity and value are inseparable.
The things that matter most in education, though, do not fit this
paradigm. They are not scarce, and yet they are extremely
valuable—indeed they are among the most valuable in human
life. They do not become scarce by being shared. Instead, they
expand and grow the more they are shared.
One of these things is knowledge. Knowledge has never been
exhausted by spreading it to more and more people. Today, it is
more abundant than at any time in the past, and it reproduces
more prolifically as it is shared. Moreover, technology has made
it possible to store knowledge efficiently and to access it
cheaply. No wonder that the economic paradigm is having
difficulty capturing and domesticating it into a well-behaved
economic commodity.
This is disconcerting for institutions that think of themselves
8. primarily as providers of information. If the knowledge is out
there, freely accessible, why then should anyone pay large sums
of money to a knowledge gatekeeper—let alone go into debt?
Today, the confrontation between free technological access and
proprietary gate-keeping is leading to turmoil about new models
of delivery in higher education.
But the idea that a college or university is a purveyor of
information is a misplaced economic metaphor. Education is not
information transfer. The educated college graduate is not
simply the same person who matriculated four years earlier with
more information or new skills. The educated graduate is a
different person—one who has developed the innate human
capacity for learning, to the point of controlling it. The
educated graduate is an independent learner, able to seek out
answers to whatever questions arise, and able to direct his or
her own learning in accordance with the challenges that life
presents in the circumstances of his or her own life.
The maturation of the student—not information transfer—is the
real purpose of colleges and universities. Of course, information
transfer occurs during this process. One cannot become a master
of one’s own learning without learning something. But
information transfer is a corollary of the maturation process, not
its primary purpose. This is why assessment procedures that
depend too much on quantitative measures of information
transfer miss the mark. It is entirely possible for an institution
to focus successfully on scoring high in rankings for
information transfer while simultaneously failing to promote the
maturation process that leads to independent learning.
It is, after all, relatively easy to measure the means used in
getting an education, to assess the learning of intermediate
skills that prepare one for a higher purpose—things like
mastering vocabulary and spelling, for instance, which help one
to communicate. It is also easy to measure the handy,
quantifiable by-products of a college education, like post-
graduate earning, either in the short term or long term. But both
of these kinds of measures fail to speak to education’s proper
9. end—the maturation of the student.
We need to move away from easy assessments that miss the
point to more difficult assessments that try to get at the
maturation process. The Gallup-Purdue Index Report entitled
“Great Jobs, Great Lives” found six crucial factors linking the
college experience to success at work and overall well-being in
the long term:
1. at least one teacher who made learning exciting
2. personal concern of teachers for students
3. finding a mentor
4. working on a long-term project for at least one semester
5. opportunities to put classroom learning into practice through
internships or jobs
6. rich extracurricular activities
We should turn all our ingenuity toward measuring factors like
these, difficult as that task might be, and use these results to
push back against easy assessments based on the categories of
economics.
Unless we stop taking the easy way, unless we get past our habit
of interpreting everything in economic terms, we will never
grasp the true value of a college education.
ESSAY #1—ILLUSTRATION
An author who writes illustrative essays exemplifies a central
idea through examples. Good examples are used to further
clarify and understand the author’s message while helping to
build a connection with readers. In formulating illustrative
essays, a writer either focuses on one specific example or uses
10. several examples in explaining the central idea.
Genre/Medium:Illustration/Typed essay
Purpose:The writer of an illustration essay uses examples to
reveal the essential characteristics of a topic and/or to reinforce
a thesis. For this assignment you will write an illustration essay
that follows the five-paragraph essay format on one of the essay
topics listed below.
Format:Your five-paragraph essay must contain a concrete
closed (parallel, three-point) thesis statement at the end of the
first paragraph and follow the MLA guidelines.
Audience:This essay will target a scholarly audience.
Therefore, your language and style should meet the intellectual
needs of individuals who read on a collegiate level. Are you
writing to an audience that consists of classmates and the
professor who have experienced similar obstacles in life
towards becoming literate scholars? As you think about your
audience, write to pique the interest of your audience by
considering what your readers already know and what they need
to know.
Stance:What attitude will you convey through illustration? Will
you portray yourself as serious, intellectual, passionate,
desensitized, or sarcastic? Think about your stance and convey
your stance throughout your essay.
Instructions:Write a five-paragraph illustration essay on one of
the topics below.
(A). In the essay “Why We Are Looking at the ‘Value’ of
College All Wrong,” Christopher
Nelson defines the educated graduate as an independent
learner who seeks “out
answers to whatever questions arises” while applying the
11. lessons he/she learns in
college to tackle life’s challenges.
Write an essay explaining ways you, as a college student,
are evolving into an
“independent learner.” Provide evidence from Nelson’s
essay to support your
assertions.
The Foundations: Logic and Proofs
Chapter 1, Part III: Proofs
Rules of Inference
Section 1.6
Revisiting the Socrates Example
We have the two premises:
“All men are mortal.”
“Socrates is a man.”
And the conclusion:
“Socrates is mortal.”
How do we get the conclusion from the premises?
12. The Argument
We can express the premises (above the line) and the conclusion
(below the line) in predicate logic as an argument:
We will see shortly that this is a valid argument.
Valid Arguments
We will show how to construct valid arguments in two stages;
first for propositional logic and then for predicate logic. The
rules of inference are the essential building blocks in the
construction of valid arguments.
Propositional Logic
Inference Rules
Predicate Logic
Inference rules for propositional logic plus additional inference
rules to handle variables, predicates, and quantifiers.
Arguments in Propositional Logic
A argument in propositional logic is a sequence of propositions.
All but the final proposition are called premises. The last
statement is the conclusion.
The argument is valid if the premises imply the conclusion. An
valid argument form is an argument that is valid no matter
what propositions are substituted into its propositional
variables.
If the premises are p1 ,p2, …,pn and the conclusion is q then
13. (p1 ∧ p2 ∧ … ∧ pn ) → q is a tautology.
Inference rules are all simple valid argument forms that will be
used to construct more complex argument forms.
Rules of Inference for Propositional Logic: Modus Ponens (MP)
Example:
Let p be “It is snowing.”
Let q be “I will study discrete math.”
“If it is snowing, then I will study discrete math.”
“It is snowing.”
“Therefore , I will study discrete math.”
Corresponding Tautology:
(p ∧ (p →q)) → q
Modus Tollens (MT)
Example:
Let p be “it is snowing.”
Let q be “I will study discrete math.”
“If it is snowing, then I will study discrete math.”
“I will not study discrete math.”
“Therefore , it is not snowing.”
14. Corresponding Tautology:
(¬q∧ (p →q))→¬p
Hypothetical Syllogism (Hyp)
Example:
Let p be “it snows.”
Let q be “I will study discrete math.”
Let r be “I will get an A.”
“If it snows, then I will study discrete math.”
“If I study discrete math, I will get an A.”
“Therefore , If it snows, I will get an A.”
Corresponding Tautology:
((p →q) ∧ (q→r)) → (p→ r)
Disjunctive Syllogism (Disj)
Example:
Let p be “I will study discrete math.”
Let q be “I will study English literature.”
“I will study discrete math or I will study English literature.”
“I will not study discrete math.”
“Therefore , I will study English literature.”
Corresponding Tautology:
15. (¬p∧ (p ∨ q))→q
Addition (Add)
Example:
Let p be “I will study discrete math.”
Let q be “I will visit Las Vegas.”
“I will study discrete math.”
“Therefore, I will study discrete math or I will visit
Las Vegas.”
Corresponding Tautology:
p →(p ∨ q)
Simplification (Simp)
Example:
Let p be “I will study discrete math.”
Let q be “I will study English literature.”
“I will study discrete math and English literature”
“Therefore, I will study discrete math.”
Corresponding Tautology:
(p∧ q) →p
16. Conjunction (Conj)
Example:
Let p be “I will study discrete math.”
Let q be “I will study English literature.”
“I will study discrete math.”
“I will study English literature.”
“Therefore, I will study discrete math and I will study English
literature.”
Corresponding Tautology:
((p) ∧ (q)) →(p ∧ q)
Resolution (Res)
Example:
Let p be “I will study discrete math.”
Let r be “I will study English literature.”
Let q be “I will study databases.”
“I will not study discrete math or I will study English
literature.”
“I will study discrete math or I will study databases.”
“Therefore, I will study databases or I will study English
literature.”
Corresponding Tautology:
((¬p ∨ r ) ∧ (p ∨ q)) →(q ∨ r)
Resolution plays an important role in AI and is used in Prolog.
17. Arguments in Propositional Logic
Each simple inference rule embodies an argument form that is
valid:
It is impossible for the premises to be true and the conclusion
false
Alternatively, in a truth table every row in which ALL of the
premises are T, the conclusion is also T
A propositional argument with a valid form is a valid argument
To show a propositional argument from invalid you need only
show that:
It is possible for the premises to ALL be true and the conclusion
false
Alternatively, in a truth table there is at least one row in which
ALL of the premises are T and the conclusion F
Using the Rules of Inference to Build Valid Arguments
A valid argument is a sequence of statements. Each statement
is either a premise or follows from previous statements by rules
of inference. The last statement is called conclusion.
A valid argument takes the following form:
S1
S2
.
.
.
Sn
C
Valid Arguments
18. Example 1: From the single proposition
Show that q is a conclusion.
Solution
:
Note: Conjunction should be Simplification
Valid Arguments
Example 2:
With these hypotheses:
“It is not sunny this afternoon and it is colder than yesterday.”
“We will go swimming only if it is sunny.”
“If we do not go swimming, then we will take a canoe trip.”
“If we take a canoe trip, then we will be home by sunset.”
Using the inference rules, construct a valid argument for the
conclusion:
“We will be home by sunset.”