short - The Short Truth-Table Method: Three Examples...

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Unformatted text preview: The Short Truth-Table Method: Three Examples Philosophy 12A June 3, 2010 1 Example #1 Page 66 #3 Answer . A (C E),B D (A B) (C (D E)) Explanation . 1 Assume that A (C E) is > , B D is > , and (A B) (C (D E)) is . In order for (A B) (C (D E)) to be , both A B and C must be > , and both D and E must be . This guarantees that the first premise is > (since A (C E) must , at this point, have a > consequent). We can also make the second premise > , simply by making B . Finally, by making A > , we can ensure that the conclusion is , which yields the following interpretation on which A (C E) and B D are > , but (A B) (C (D E)) is ( i.e. , the following counterexample to validity). A B C D E A (C E) B D (A B) (C (D E)) > > > > > > > > > > Therefore, by the definition of...
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