Copyright © 2008 Pearson Education, Inc. Chapter 1.

Slides:



Advertisements
Similar presentations
9/2/2008 Warm Up Complete the conjecture by looking for a pattern in the diagram below. The number of sides of a polygon that has n vertices is________________.
Advertisements

Chapter 3 Introduction to Logic © 2008 Pearson Addison-Wesley.
3.5 – Analyzing Arguments with Euler Diagrams
PROOF BY CONTRADICTION
When several examples form a pattern and you assume the pattern will continue, you are applying inductive reasoning. Inductive reasoning is the process.
 Writing conditionals  Using definitions as conditional statements  Writing biconditionals  Making truth tables.
Chapter 1 The Logic of Compound Statements. Section 1.3 Valid & Invalid Arguments.
Chapter 1 The Logic of Compound Statements. Section 1.2 – 1.3 (Modus Tollens) Conditional and Valid & Invalid Arguments.
Copyright © 2015, 2011, 2008 Pearson Education, Inc. Chapter 1, Unit 1B, Slide 1 Thinking Critically 1.
Chapter 3 Introduction to Logic © 2008 Pearson Addison-Wesley.
Syllabus Every Week: 2 Hourly Exams +Final - as noted on Syllabus
SEVENTH EDITION and EXPANDED SEVENTH EDITION
Copyright © 2005 Pearson Education, Inc. Slide 1-1.
Chapter 3 Section 5 - Slide 1 Copyright © 2009 Pearson Education, Inc. AND.
Adapted from Discrete Math
1.1 Sets and Logic Set – a collection of objects. Set brackets {} are used to enclose the elements of a set. Example: {1, 2, 5, 9} Elements – objects inside.
Chapter 3 Section 4 – Slide 1 Copyright © 2009 Pearson Education, Inc. AND.
Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 3.3, Slide Logic The Study of What’s True or False or Somewhere in Between.
Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 3.3, Slide Logic The Study of What’s True or False or Somewhere in Between.
Chapter 8 Logic DP Studies. Content A Propositions B Compound propositions C Truth tables and logical equivalence D Implication and equivalence E Converse,
CH1 – 3 REVIEW Summary. CHAPTER 1: 1A RECOGNIZING FALLACIES KEY TERMS AND KEY IDEAS AND SKILLS  Key Terms  Logic  Argument – premises, conclusions.
Chapter 3 Section 3 - Slide 1 Copyright © 2009 Pearson Education, Inc. AND.
The Inverse Error Jeffrey Martinez Math 170 Dr. Lipika Deka 10/15/13.
Geometry CH 4-1 Using Logical Reasoning Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz.
Recognizing Fallacies.  Logic ◦ The study of the methods and principles of reasoning  Premises ◦ Facts or assumptions  Fallacy ◦ A deceptive argument-
Chapter 3 Introduction to Logic © 2008 Pearson Addison-Wesley. All rights reserved.
Lecture 4. CONDITIONAL STATEMENTS: Consider the statement: "If you earn an A in Math, then I'll buy you a computer." This statement is made up of two.
Chapter 3: Introduction to Logic. Logic Main goal: use logic to analyze arguments (claims) to see if they are valid or invalid. This is useful for math.
Aerospace Engineering Laboratory I
Unit 01 – Lesson 07 – Conditional Statements
Thinking Mathematically Arguments and Truth Tables.
Venn Diagrams Truth Sets & Valid Arguments Truth Sets & Valid Arguments Truth Tables Implications Truth Tables Implications Truth Tables Converse, Inverse,
DEDUCTIVE ARGUMENTS The aim of this tutorial is to help you learn to recognize, analyze, and evaluate deductive arguments.
 2012 Pearson Education, Inc. Slide Chapter 3 Introduction to Logic.
Sentence (syntactically Independent grammatical unit) QuestionCommandStatement “This is a class in logic.” “I enjoy logic.” “Today is Friday.”
Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 3.4, Slide 1 3 Logic The Study of What’s True or False or Somewhere in Between 3.
Slide Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.
 2012 Pearson Education, Inc. Slide Chapter 3 Introduction to Logic.
If-then statements April 4, What is an if-then statement? One of the postulates we looked at earlier stated: If B is between A and C, then AB +
CONDITIONAL STATEMENTS Intro to AlgebraFarris 2015.
Copyright © 2011 Pearson Education, Inc. Thinking Critically.
Introduction to Logic © 2008 Pearson Addison-Wesley.
Introduction to Deductive Proofs
Objectives Identify, write, and analyze the truth value of conditional statements. Write the inverse, converse, and contrapositive of a conditional statement.
2. The Logic of Compound Statements Summary
Conditional Statements
2-1 Vocabulary conditional statement hypothesis/conclusion
Jeffrey Martinez Math 170 Dr. Lipika Deka 10/15/13
Objectives Identify, write, and analyze the truth value of conditional statements. Write the inverse, converse, and contrapositive of a conditional statement.
Principles of Computing – UFCFA3-30-1
Chapter 8 Logic Topics
Pearson Unit 1 Topic 2: Reasoning and Proof 2-2: Conditional Statements Pearson Texas Geometry ©2016 Holt Geometry Texas ©2007.
2 Chapter Introduction to Logic and Sets
Chapter 3 Introduction to Logic 2012 Pearson Education, Inc.
Chapter 3 Introduction to Logic © 2008 Pearson Addison-Wesley.
Copyright © 2014 Pearson Education, Inc.
Chapter 3 Introduction to Logic 2012 Pearson Education, Inc.
Thinking Critically Copyright © 2011 Pearson Education, Inc.
Chapter 3 Introduction to Logic 2012 Pearson Education, Inc.
1 Chapter An Introduction to Problem Solving
Chapter 3 Introduction to Logic 2012 Pearson Education, Inc.
1 Chapter An Introduction to Problem Solving
Chapter 2.2 Notes: Analyze Conditional Statements
Chapter 3 Introduction to Logic © 2008 Pearson Addison-Wesley.
CHAPTER 3 Logic.
2-3 Conditional Statements
Math Humor Teacher: Which month has 28 days? Student: All of them!!
Chapter 3 Introduction to Logic © 2008 Pearson Addison-Wesley.
Propositional Logic 1) Introduction Copyright 2008, Scott Gray.
ID1050– Quantitative & Qualitative Reasoning
Presentation transcript:

Copyright © 2008 Pearson Education, Inc. Chapter 1

Copyright © 2008 Pearson Education, Inc. Slide 1-3 Recognizing Fallacies 1-A Which of the following describes an argument based on the idea that since one event preceded another event, the first event must have caused the second? a) Hasty generalization b) Limited choice c) False cause d) Appeal to ignorance

Copyright © 2008 Pearson Education, Inc. Slide 1-4 Recognizing Fallacies 1-A Which of the following describes an argument based on the idea that since one event preceded another event, the first event must have caused the second? a) Hasty generalization b) Limited choice c) False cause d) Appeal to ignorance

Copyright © 2008 Pearson Education, Inc. Slide 1-5 Recognizing Fallacies 1-A Which of the following describes an argument based on the idea that since something has not been proved to be false, it must therefore be true? a) Hasty generalization b) Limited choice c) Diversion (red herring) d) Appeal to ignorance

Copyright © 2008 Pearson Education, Inc. Slide 1-6 Recognizing Fallacies 1-A Which of the following describes an argument based on the idea that since something has not been proved to be false, it must therefore be true? a) Hasty generalization b) Limited choice c) Diversion (red herring) d) Appeal to ignorance

Copyright © 2008 Pearson Education, Inc. Slide 1-7 Propositions and Truth Values 1-B Which of the following is not a proposition? a) Amy has green eyes. b) What is your IQ? c) = 15 d) Toads can sing opera.

Copyright © 2008 Pearson Education, Inc. Slide 1-8 Propositions and Truth Values 1-B Which of the following is not a proposition? a) Amy has green eyes. b) What is your IQ? c) = 15 d) Toads can sing opera.

Copyright © 2008 Pearson Education, Inc. Slide 1-9 Propositions and Truth Values 1-B If p is false and q is false, then which of the following is true? a) p or not q b) p and not q c) p or q d) p and q

Copyright © 2008 Pearson Education, Inc. Slide 1-10 Propositions and Truth Values 1-B If p is false and q is false, then which of the following is true? a) p or not q b) p and not q c) p or q d) p and q

Copyright © 2008 Pearson Education, Inc. Slide 1-11 Conditional 1-B if p, then q Alternative Phrasings p is sufficient for qp will lead to qp implies q q is necessary for pq if pq whenever p

Variations on the Conditional Conditional if p, then q If you are sleeping, then you are breathing. Converse if q, then p If you are breathing, then you are sleeping. Copyright © 2008 Pearson Education, Inc. Slide B

Variations on the Conditional Conditional if p, then q If you are sleeping, then you are breathing. Inverse if not p, then not q If you are not sleeping, then you are not breathing. Copyright © 2008 Pearson Education, Inc. Slide B

Variations on the Conditional Conditional if p, then q If you are sleeping, then you are breathing. Contrapositive if not q, then not p If you are not breathing, then you are not sleeping. Copyright © 2008 Pearson Education, Inc. Slide B

Variations on the Conditional Conditional and the Contrapositive Have the same truth tables, thus are logically equivalent! Converse and Inverse Have the same truth tables, thus are logically equivalent! Copyright © 2008 Pearson Education, Inc. Slide B

Copyright © 2008 Pearson Education, Inc. Slide 1-16 Sets and Venn Diagrams 1-C Which of the following sets are not disjoint? a) Mothers and sons b) Mothers and daughters c) Mothers and fathers d) Fathers and daughters

Copyright © 2008 Pearson Education, Inc. Slide 1-17 Sets and Venn Diagrams 1-C Which of the following sets are not disjoint? a) Mothers and sons b) Mothers and daughters c) Mothers and fathers d) Fathers and daughters

Copyright © 2008 Pearson Education, Inc. Slide 1-18 Sets and Venn Diagrams 1-C Use the Venn diagram below to find out how many people ordered cake. a) 8 b) 6 c) 12 d) 14 Deserts CakeIce cream

Copyright © 2008 Pearson Education, Inc. Slide 1-19 Sets and Venn Diagrams 1-C Use the Venn diagram below to find out how many people ordered cake. a) 8 b) 6 c) 12 d) 14 Deserts CakeIce cream

Copyright © 2008 Pearson Education, Inc. Slide 1-20 Analyzing Arguments 1-D All cats have four legs. Some cats are white. Some four-legged animals are white. Which of the following describes this argument? a) Valid and sound b) Not valid and sound c) Valid and not sound d) Not valid and not sound

Copyright © 2008 Pearson Education, Inc. Slide 1-21 Analyzing Arguments 1-D All cats have four legs. Some cats are white. Some four-legged animals are white. Which of the following describes this argument? a) Valid and sound b) Not valid and sound c) Valid and not sound d) Not valid and not sound

Copyright © 2008 Pearson Education, Inc. Slide 1-22 Analyzing Arguments 1-D Use inductive reasoning to test the following mathematical rules. Which statement do you think is false? a) b) c)d)

Copyright © 2008 Pearson Education, Inc. Slide 1-23 Analyzing Arguments 1-D Use inductive reasoning to test the following mathematical rules. Which statement do you think is false? a) b) c)d)

Copyright © 2008 Pearson Education, Inc. Slide 1-24 Critical Thinking in Everyday Life 1-E Which of the following are stated explicitly in an argument? a) Hidden assumptions b) Missing information c) Valid premises d) Other possible conclusions

Copyright © 2008 Pearson Education, Inc. Slide 1-25 Critical Thinking in Everyday Life 1-E Which of the following are stated explicitly in an argument? a) Hidden assumptions b) Missing information c) Valid premises d) Other possible conclusions

Copyright © 2008 Pearson Education, Inc. Slide 1-26 Critical Thinking in Everyday Life 1-E To help make a complex argument clear, visual aids may include all except which of the following? a) Written descriptions b) Venn diagrams c) Graphs d) Flow charts

Copyright © 2008 Pearson Education, Inc. Slide 1-27 Critical Thinking in Everyday Life 1-E To help make a complex argument clear, visual aids may include all except which of the following? a) Written descriptions b) Venn diagrams c) Graphs d) Flow charts