CHAPTER 3 Summary 167 Section 3.2 & Section 3.3 Basic Truth Tables Negation Conjunction Disjunction Conditional Biconditional p p~ p q p q ∧ p q ∨ p q → p q ↔ T F T T T T T T F T T F F T F F F T F T T F F F F F T T Examples 1–10, pages 110–118 Examples 1–10, pages 122–128 Section 3.4 De Morgan’s Laws p q p q p q p q ~( ) ~ ~ ~( ) ~ ~ ∧ ⇔ ∨ ∨ ⇔ ∧ Other Equivalent Forms p q p q p q p q p q p q q p ~ ~( ) ~ ( ) ( ) [ ] → ⇔ ∨ → ⇔ ∧ ↔ ⇔ → ∧ → Variations of the Conditional Statement Name Symbolic Form Read Conditional →p q If p, then q. Converse of the conditional →q p If q, then p. Inverse of the conditional p q ~ ~ → If not p, then not q. Contrapositive of the conditional q p ~ ~ → If not q, then not p. Examples 4– 6, pages 134–135 Examples 7–9, pages 136–137 Examples 10–12, pages 138–139 Section 3.5 Standard Forms of Valid Arguments Law of Law of Law of Disjunctive Detachment Contraposition Syllogism Syllogism →p q →p q →p q ∨p q p q ∴ q p ~ ~∴ q r p r → ∴ → p q ~ ∴ Standard Forms of Invalid Arguments Fallacy of the Fallacy of the Converse Inverse →p q →p q q p ∴ p q ~ ~ ∴ Examples 1– 4, pages 146–148 Example 5, page 149 Section 3.5 & Section 3.6 Symbolic Argument Versus Syllogistic Argument Words or Method of Phrases Used Determining Validity Symbolic and, or, not, Truth tables or by argument if–then, comparison with if and only if standard forms of arguments Syllogistic all are, Euler diagrams argument some are, none are, some are not Examples 1–5, pages 146–149 Examples 1– 6, pages 155–158
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