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This document discusses the basics of propositional logic. It defines propositions or statements as the basic units of propositional logic. Compound propositions are formed when simple propositions are connected with logical connectives like "and" and "or". A proposition must always be able to be validated as true or false. It provides examples of true, false, and non-valid propositions. Propositional variables are used to represent unspecified statements. Logical equivalences are compound propositions that have the same logical content. Predicates are parts of statements that can be affected by variables. Quantifiers like universal, existential, and uniqueness are used to represent logical quantities.
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Follow on Facebook:
https://web.facebook.com/learnforgood...
and on Youtube:
https://www.youtube.com/channel/UC8kUyEAA5ix6Bl5H5gKXo3A
Like, Comment and Share.
Also Subscribe For More Videos.
Learn For Good.
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The document discusses propositional logic including:
- Propositional logic uses propositions that can be either true or false and logical connectives to connect propositions.
- It introduces syntax of propositional logic including atomic and compound propositions.
- Logical connectives like negation, conjunction, disjunction, implication, and biconditional are explained along with their truth tables and significance.
- Other concepts discussed include precedence of connectives, logical equivalence, properties of operators, and limitations of propositional logic.
- Examples are provided to illustrate propositional logic concepts like truth tables, logical equivalence, and translating English statements to symbolic form.
Logic.pptx
This document provides information about logic and mathematical logic. It begins by asking the reader to answer 10 logic questions. It then defines key logical terms and concepts like propositions, truth tables, logical connectives, and logical operators like negation, conjunction, and disjunction. It provides examples and explanations of how to determine the truth value of simple and compound propositions using truth tables and logical operators. The document aims to explain the foundations and basic components of propositional logic.
desmath(1).ppt
This document provides an overview of a course on discrete mathematics. The course objectives are to develop mathematical reasoning skills, learn how to analyze counting problems, and learn how to specify and analyze algorithms. Topics covered include formal logic, proofs, sets and combinatorics, algorithms and complexity, induction, counting, discrete probability, relations, graphs and trees, Boolean algebra, and finite-state and Turing machines. The primary textbook is Discrete Mathematics and Its Applications by Rosen. Chapter 1 covers propositional logic, including logical connectives like negation, conjunction, disjunction, implication, equivalence, and truth tables. Propositional equivalences like De Morgan's laws are also discussed. Bit operations on strings of Boolean values are introduced.
Chapter 1
The document summarizes key concepts in propositional logic including:
1. Propositions are declarative sentences that are either true or false. Logical operators like negation, conjunction, disjunction, implication and biconditional are used to combine propositions.
2. Truth tables are used to determine the truth value of compound propositions based on the truth values of the individual propositions.
3. De Morgan's laws provide equivalences for negating conjunctions and disjunctions.
Chapter 1
The document summarizes key concepts in propositional logic including:
1. Propositions are declarative sentences that are either true or false. Logical operators like negation, conjunction, disjunction, implication and biconditional are used to combine propositions.
2. Truth tables are used to determine the truth value of compound propositions based on the truth values of the individual propositions.
3. De Morgan's laws provide equivalences for negating conjunctions and disjunctions.
Meaning and Logic.pptx
The document discusses logical concepts such as meaning, truth, negation, and logical relations between sentences and words. It provides examples to illustrate key logical principles like the principle of polarity, which states that a sentence is either true or false; negation, where negating a sentence reverses its truth value; and logical relations like entailment, equivalence, contradiction, and independence. Logical relations depend on the truth conditions of sentences rather than their literal meanings. Predicate terms can have logical relations like equivalence if they have the same denotation, and subordination if one term is true of arguments whenever another term is true of them.
predicateLogic.ppt
Propositional logic and predicate logic are knowledge representation languages used in AI. Propositional logic uses symbols to represent simple statements, while predicate logic (first-order logic) is more expressive and commonly used, using predicates, quantifiers and variables to represent relationships about objects in the world. Some key aspects of first-order logic include its syntax, semantics, how it can represent statements about universality and existence using quantifiers, and how it can be used to formally represent real-world knowledge and relationships.
20220818151924_PPT01 - The Logic of Compound and Quantitative Statement.pptx
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
Logic
The document discusses key concepts in logic including propositions, truth tables, logical connectives like conjunction and disjunction, quantifiers, and valid arguments. Some key points:
- A proposition is a statement that is either true or false.
- Truth tables define the truth values of logical connectives and conditionals.
- Quantifiers like "all" and "some" are used to make generalized statements about sets.
- Venn diagrams can represent relationships between sets graphically.
- An argument is valid if the premises necessarily make the conclusion true.
proposition, truth tables and tautology.pptx
This document defines key concepts in propositional logic including propositions, arguments, validity, and fallacies. It explains how to represent arguments using premises and conclusions. It also defines truth tables and how they are used to determine the truth value of compound statements for all possible combinations of true and false basic statements. Truth tables are provided for negation, conjunction, disjunction, implication, tautologies, and contradictions. An example shows how to identify a tautology and contradiction using truth tables. Exercises are provided to have the reader construct truth tables.
proposition Logic-1.pptx Discrete Mathematics
This document provides an overview of propositional logic concepts including:
1. Propositions are declarative sentences that are either true or false. Conventional letters like p, q, r are used to represent propositions.
2. Logical connectives like negation, conjunction, disjunction, conditional, biconditional are defined along with their truth tables.
3. Quantifiers like universal and existential are introduced. Universal quantification ∀x p(x) means p(x) is true for all x, while existential quantification ∃x p(x) means there exists an x where p(x) is true.
Prove asymptotic upper and lower hounds for each of the following sp.pdf
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.
Symbolic logic
This document discusses the basics of symbolic logic, including:
1. Statements can be true or false, while questions and commands are not statements. Variables refer to unspecified elements while constants refer to specific elements.
2. Connectives like negation, disjunction, conjunction, implication, and biconditional are used to combine statements and change their truth values.
3. Quantifiers like "all" and "some" are used to make statements about variables. Validity refers to whether a conclusion necessarily follows from given premises. Formal systems of logic aim to prove validity through formal rules of inference.
Unit-4-Knowledge-representation.pdf
Notes for CSIT, AI.
This gives an comprehensive overview of the topic Knowledge Representation of the Artificial Intelligence.
Math
The document discusses propositional logic and covers topics like propositional variables, truth tables, logical equivalence, predicates, and quantifiers. It defines key concepts such as propositions, tautologies, contradictions, predicates, universal and existential quantifiers. Examples are provided to illustrate different types of truth tables, logical equivalences like De Morgan's laws, and uses of quantifiers.
LOGICAL CONNETIVES USE DISCRETE MATHSMATICS ASSINGMENT
This document discusses logical connectives and their use in natural and formal languages. It defines logical connectives as symbols that connect propositions such that the truth value of the resulting statement depends only on the input propositions and the connective. In natural language, words like 'and' and 'or' can serve as logical connectives, but words like 'so' are not always logical. There are 5 basic logical connectives - negation, conjunction, disjunction, conditional, and biconditional - along with their truth tables and examples. Logical connectives allow for logical reasoning and have applications in computer science.
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PowerPoint Presentation
- 2. PROPOSITIONAL LOGIC Proposition or statements, are also known as simple sentences makes up the basic units for propositional logic. When two or more simple sentences are related through connectives, it forms a more complicated proposition called compound sentence. A statement / propositions must always be able to be validated as True (T) or False (F).
- 3. EXAMPLE: i) All fathers are men. This statement is true because only man can be father. ii) All men are father. This statement is false because only those men who are married and have kids are fathers. Single men are not father. iii) I like Monday. This sentence is neither true nor false as it does not include a fact. The notion of ‘liking Monday’ is entirely depending on the particular individual. Some may like it. Some may not. Sentence which are neither true nor false are not propositions.
- 4. PROPOSITIONAL VARIABLES Propositional variables are used to stand for unspecified statements. Means that each variable assigned may or may not have connection between them.
- 5. EXAMPLE: i) She likes dancing. ii) She likes camping. Iii) She likes outdoor activities. Each variable is assigned to a statement.
- 6. PROSITIONAL EQUIVALENCE Tautology • A compound proposition that is always true Contradiction • A compound proposition that is always false Contingency • A compound proposition that is neither a tautology nor a contradiction.
- 7. EXAMPLE: LOGICAL EQUIVALENCES • Compound proposition that have the same logical content. Means, compound propositions p and q are called logically equivalent if p ↔ q is a tautology.
- 8. PREDICATES In some situations, a statement can be composed of two parts, the variable and the predicates.
- 9. EXAMPLE: The cost of an apple is RM x. (In this case, the cost of the apple is a predicate, while x is the variable which represents the price.) The above statement can also be expressed as propositional function P at the value of x, which is P(x), Where P[the cost of an apple] is affected by x[the price]. Note: Predicate is not a proposition until variable is declared on it. P itself is not a proposition until it is bound by x, forming P(x).
- 10. QUADTIFIERS Universal Quantifier • ∀ is used to represent ‘for all’ Existential Quantifier • ∃ is used to represent ‘for some state / value of’ Uniqueness Quantifier • ∃! Is used to represent ‘for one and only one x’