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Unformatted text preview: Chapter 5: Hints and Selected Solutions Section 5.1 (page 131) 5.1 The pattern From P ∨ Q and ¬ P , infer Q is valid. If P ∨ Q is true, then by the truth table for ∨ , at least one of P or Q must be true. But if ¬ P is true, then by the truth table for ¬ , P must be false. Hence, it must be that Q is true. 5.2 The pattern From P ∨ Q and Q , infer ¬ P is not valid. To see an example of how it could lead from true conclusions to false ones, consider the following argument: Washington or Lincoln was president of the U.S. Lincoln was president of the U.S. Washington was not president of the U.S. This argu ment has true premises and false conclusion, but has the form of the displayed pattern. What makes the form tempting is the fact that peo ple often read ∨ as exclusive disjunction. Section 5.2 (page 134) 5.7 Here is an informal proof of the following argument: Home ( max ) ∨ Home ( claire ) ¬ Home ( max ) ∨ Happy ( carl ) ¬ Home ( claire ) ∨ Happy ( carl ) Happy ( carl...
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 Spring '09
 dhoe
 Logic, Claire

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