Main Goals for Chapter 3

• To become familiar with basic concepts from logic: statements (simple and compound), quantifiers (universal and existential)
• To use truth tables for different kinds of statements
• To become familiar with different kinds of compound statements: conjunction (and), disjunction (or), negation (not)
• To show when statements are equivalent by looking at their truth tables, or by using De Morgan's Laws
• To understand the conditional (if p then q), different ways to word a conditional, when a conditional is true and when it is false, what the conditional is equivalent to, what the negation of a conditional is
• To become familiar with statements related to the conditional: converse, inverse and contrapositive
• How to analyze arguments with Euler Diagrams or with truth tables

Section 3.1 Statements and Quantifiers. Key Ideas: statements (simple and compound), logical connectives (and their symbols), negations, quantifiers (existential and universal).  Sample exercises (pages 99-101): 1-31 (odd), 39-63 (odd), 75

Section 3.2  Truth Tables and Equivalent Statements.  Key Ideas: truth tables for conjunction, disjunction, negation, when statements are equivalent, number of rows, De Morgan's Laws for negations.  Sample exercises (pages 111-112): 1-17 (odd), 37-69 (odd)

Section 3.3  The Conditional and Circuits.  Key Ideas: the conditional (if p, then q), equivalent to a disjunction, negation of the conditional.  Won't be doing circuits. Sample exercises (pages 120-122): 1-19 (odd), 27-63 (odd), 67-83 (odd)

Section 3.4  More on the Conditional.  Key Ideas: converse, inverse, contrapositive, translations of the conditional.  Sample exercises (pages 128-129):  1-15 (odd), 19-41 (odd)

Section 3.5 Analyzing Arguments with Euler Diagrams.  Key Ideas: valid and invalid arguments, using Euler diagrams.  Sample exercises (pages 132-133): 1-31 (odd)

Section 3.6 Analyzing Arguments with Truth Tables.  Key Ideas: testing validity with a truth table, common valid forms (modus ponens, modus tollens, disjunctive syllogism, reasoning by transitivity), common fallacies (fallacy of the converse, fallacy of the inverse).  Sample exercises (pages 146-148): 1-21 (odd), 27-35 (odd), 39-49 (odd)

Chapter 3 Slides

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last updated October 19, 2011