Solutions05 - Chapter 5 Hints and Selected Solutions...

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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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Solutions05 - Chapter 5 Hints and Selected Solutions...

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