short method truth tables

short method truth tables - Three Model Answers Involving...

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Three Model Answers Involving the “Short” Method of Constructing Interpretations Philosophy 12A September 23, 2008 1 Example #1 — Page 66 #3 Answer . A (C E),B D ø (A B) (C (D E)) Explanation . 1 Assume that ‘ A (C E) ’ is true, ‘ B D ’ is true, and ‘ (A B) (C (D E)) ’ is false. In order for (A B) (C (D E)) ’ to be false, both ‘ A B ’ and ‘ C ’ must be true, and both ‘ D ’ and ‘ E ’ must be false. This guarantees that the first premise is true (since ‘ A (C E) must , at this point, have a true consequent). We can also make the second premise true, simply by making ‘ B ’ false. So, as the following single-row truth-table shows, we have succeeded in finding an interpretation on which ‘ A (C E) ’ and ‘ B D ’ are both true, but ‘ (A B) (C (D E)) ’ is false. A B C D E A (C E) B D (A B) (C (D E)) > > > > Therefore, by the definition of ± , A (C E),B
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