Inductivereasoning and deductive 2013
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1. The document provides examples of identifying patterns in sequences and numbers. It discusses using inductive and deductive reasoning to make conjectures about patterns and find counterexamples. 2. The objectives are to find the next term in given sequences, provide counterexamples to disprove statements, and draw conclusions from given information using deductive reasoning. 3. Examples are given of identifying the next terms in patterns like months of the year, multiples of numbers, and progressively smaller decimal values. Inductive reasoning is used to form conjectures about continuing patterns while deductive reasoning draws conclusions from given facts.
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The document discusses the importance of finding patterns and using inductive reasoning in geometry and mathematics. It provides examples of describing patterns, making conjectures based on examples, and using inductive reasoning to form hypotheses about general cases. Students are instructed on how to look for patterns, make conjectures, and verify or find counterexamples for conjectures.
Module 3_Problem Solving With Logic.pptx
The document provides an overview of problem solving techniques including:
- Using inductive and deductive reasoning to evaluate arguments and solve problems.
- Identifying patterns in sequences to derive nth term formulas.
- Applying Polya's four-step problem solving strategy of understanding the problem, devising a plan, carrying out the plan, and reviewing the solution.
- Using work principles and a five-step process to systematically solve problems.
Examples are provided to illustrate each technique.
Reasoning
The document discusses different types of reasoning including inductive reasoning and deductive reasoning. It provides examples of each type of reasoning and how they are used. Inductive reasoning involves making generalizations based on specific examples, while deductive reasoning uses general statements to logically prove a specific conclusion. The document explains how to use Venn diagrams to determine if a deductive argument is valid or invalid.
Gch2 l1
This document discusses inductive reasoning and making conjectures based on patterns. It provides examples of identifying patterns, making conjectures based on examples, and finding counterexamples to disprove conjectures. The key steps of inductive reasoning are outlined as looking for a pattern, making a conjecture, and proving or disproving the conjecture. Examples include patterns of numbers, geometry shapes, biology data on whale sizes, and properties of numbers.
Geometry Section 2-1
This document discusses inductive reasoning and making conjectures. It provides examples of using inductive reasoning to find patterns in sequences and geometric relationships. A conjecture is a conclusion reached through inductive reasoning. A counterexample can disprove a conjecture by showing it is not universally true. The document gives examples of making conjectures based on examples and finding a counterexample to disprove a statement.
Geometry Section 2-4 1112
This document provides an overview of deductive reasoning, including the Law of Detachment and Law of Syllogism. It defines deductive reasoning as using facts, rules, and definitions to reach a logical conclusion. The Law of Detachment states that if p implies q is true and p is true, then q must be true. The Law of Syllogism states that if p implies q and q implies r are both true, then p implies r must be true. The document provides examples and problems applying these laws of deductive reasoning.
Geometry Section 2-3
This document provides information on deductive reasoning and the laws of detachment and syllogism. It defines deductive reasoning as using facts and rules to reach a logical conclusion. The law of detachment states that if p implies q and p is true, then q must be true. The law of syllogism states that if p implies q and q implies r, then p implies r. The document includes examples applying these concepts and determining whether conclusions are valid deductive reasoning or not.
Ch1-L3.1-Inductive-and-Deductive-Reasoning.pptx
This document discusses inductive and deductive reasoning. It provides examples to illustrate the differences between inductive and deductive reasoning. Inductive reasoning involves making a generalization based on specific examples, while deductive reasoning uses stated assumptions or principles to logically deduce conclusions. The document cautions that conclusions based on inductive reasoning may be incorrect, as they are conjectures rather than proven statements, and a single counterexample can invalidate a conjecture.
Geometry 201 unit 2.4
This document discusses deductive reasoning and how to evaluate arguments using deductive logic. It introduces the law of detachment and law of syllogism as valid forms of deductive reasoning. Examples are provided to illustrate identifying the hypothesis and conclusion of conditionals, and determining whether conjectures follow validly from given information using the laws of detachment and syllogism. Practice problems are included for the reader to apply these concepts.
TPCMFinalACone
This document describes the construction and demonstration of a Ternary Prediction Classification Model (TPCM) for determining the predictive capabilities of mathematical models. The author first defines key concepts like testability and degrees of confidence in observations and predictions. He then outlines current techniques for obtaining confidence in predictions, including data-oriented modeling, theoretical modeling, and hybrid approaches. Finally, the author constructs the TPCM, which aims to integrate experimental uncertainty with mathematical operations to allow models and data to be evaluated using the same framework. In Section 2, the author will demonstrate the TPCM using Hooke's law and experimental data, and in Section 3 will discuss conclusions and possible objections.
2.1.ppt
This document is from a geometry textbook and discusses inductive reasoning and making conjectures. It begins with examples of identifying patterns and making conjectures based on those patterns. It then discusses using inductive reasoning to draw conclusions from patterns and defines a conjecture as a statement believed to be true based on inductive reasoning. The document provides examples of making conjectures and finding counterexamples to disprove conjectures. It emphasizes that a single counterexample is enough to show a conjecture is false, while a conjecture needs to be proven to be shown as always true.
Geo 1.1 Patterns And Inductive Reasoning
The document discusses patterns and inductive reasoning. It defines inductive reasoning as making conjectures based on observed patterns. There are three stages of inductive reasoning: finding a pattern in examples, making a conjecture, and verifying the conjecture by showing it is true for all cases. The document provides examples of patterns and using inductive reasoning to make conjectures about patterns.
The University of Maine at Augusta Name ______.docx
The University of Maine at Augusta Name: ________________________
Mathematics Department Date: _________________________
MAT 280 F16 Location:______________________
MAT 280
Exam 1 Chapter 1.1-1.6
Please answer the following questions. Part credit is possible if the work indicates an understanding of
the objective under investigation. Students may use their laptops, tablets, textbooks, notes, calculators
and scrap paper. If used, scrap paper should be turned in with the exam. Students may not use smart
phones. If available homework should be turned in with the exam.
Time: 2:45 If staff is available, extra time is permitted.
1. Find a proposition with the given truth table.
p q ?
T T F
T F T
F T T
F F T
2. Write the truth table for the proposition (r q) (p → r). Use as many columns as necessary.
Label each column.
p Ans: p q r
T T T
T T F
T F T
T F F
F T T
F T F
F F T
F F F
Name: ________________________
3. Find a proposition using only pq and the connective V with the given truth table.
p
q
?
T T F
T F F
F T F
F F T
4. Determine whether p (q r) is equivalent to q (p r). Use as many columns as necessary.
Label each used column. Credit will only be when a completed truth table accompanies the answer.
p Ans: p q r
T T T
T T F
T F T
T F F
F T T
F T F
F F T
F F F
Name: ________________________
5. Write a proposition equivalent to ( p q) using only pq and the connective . . Support your
answer with a truth table. If necessary, insert columns in the truth table below to support your
answer
p
q
T T
T F
F T
F F
6. Prove that q p and its contrapositive are logically equivalent. If they are not equivalent, explain
why. Do the same for its inverse.
p
q
p
q
T T T T
T F T F
F T F T
F F F F
7. In the questions below write the statement in the form “If …, then ….”
a. Whenever the temperature drops below 35 degrees, children should wear boots
during recess.
b. You have completed your program’s requirements only if you are eligible to graduate.
Name: ________________________
8. Write the contrapositive, converse, and inverse of the following:
If I have a valid passport, I will be able to travel to Cuba.
.
a. Contrapositive:
b. Converse:
c. Inverse:
9. How many rows are required to show the truth table for the following compound proposition?
(q r ) → (p s) ...
Chapter 2 section 1
The document discusses inductive reasoning and pattern recognition, encouraging the reader to make conjectures based on examples given. It explains what a conjecture and counter example are, and provides examples of finding patterns to make conjectures and testing conjectures with potential counter examples. The document concludes with assigning related homework problems from the chapter.
Cross product
The document discusses the cross product of two vectors. Some key points:
- The cross product requires both vectors to be three-dimensional and results in another vector, unlike the dot product which results in a number.
- The formula for the cross product is derived using determinants. Two methods - using cofactors or copying columns - provide the formula.
- The direction of the cross product follows the right-hand rule and is orthogonal to both original vectors, unless they are parallel.
- The cross product can be used to find a vector orthogonal to a plane defined by three points, and to determine if three vectors lie in the same plane.
1.3.1B Inductive Reasoning
Use inductive reasoning to identify patterns and make conjectures
Find counterexamples to disprove conjectures
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The University of Maine at Augusta Name ______.docx
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Inductivereasoning and deductive 2013
- 1. GT Geometry Drill10/3/13 1. What are the next two terms in the sequence? 1, 4, 9, 16... 2. Write a counterexample for the following statement: For any number m, 3m is odd.
- 2. Accept the two statements as given information. State the conclusion based on the information. • 1. AB is longer than BC; BC is longer than CD • 2. 12 is greater than integer M. M is greater than 8 • 3. 4x + 6 = 14, then x =?
- 3. Use inductive and deductive reasoning to identify patterns and make conjectures. Find counterexamples to disprove conjectures. Objectives
- 4. Find the next item in the pattern. Example 1A: Identifying a Pattern January, March, May, ... The next month is July. Alternating months of the year make up the pattern.
- 5. Find the next item in the pattern. Example 1B: Identifying a Pattern 7, 14, 21, 28, … The next multiple is 35. Multiples of 7 make up the pattern.
- 6. Find the next item in the pattern. Example 1C: Identifying a Pattern In this pattern, the figure rotates 90° counter- clockwise each time. The next figure is .
- 7. Check It Out! Example 1 Find the next item in the pattern 0.4, 0.04, 0.004, … When reading the pattern from left to right, the next item in the pattern has one more zero after the decimal point. The next item would have 3 zeros after the decimal point, or 0.0004.
- 8. When several examples form a pattern and you assume the pattern will continue, you are applying inductive reasoning. Inductive reasoning is the process of reasoning that a rule or statement is true because specific cases are true. You may use inductive reasoning to draw a conclusion from a pattern. A statement you believe to be true based on inductive reasoning is called a conjecture.
- 9. Deductive reasoning is the process of using logic to draw conclusions from given facts, definitions, and properties.