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Lecture 4

PHL105Y5 Lecture 4: Exercise 3.4 A Answers

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Bernard Katz

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Exercise 3.4A 1 is done for illustration. 1. 1. If P, then not-C. Premise 2. C Premise 3. Either P or D Premise 4. Not-not-C 2 DN 5. Not-P 1, 4 MT 6. D 5, 6 DS Note: If P, then not-C. C ˆ Not-P may appear to be an instance of modus tollens, but it is not. One of the premises is indeed a conditional, as required by modus tollens. 2. 1. If not-B, then both A and not-C. Premise 2. Not-either D or B. Premise 3. Not-D and not-B. 2 DeM 4. Not-B. S 3 5. A and not-C. 1, 4 MP 6. Not-C S 5 3. 1. If F or G, then not-H. Premise 2. Either I or F. Premise 3. Not-I. Premise 4. F 2, 3 DS 5. F or G. 4 Add 6. Not-H 1, 5 MP 4. 1. Either K or if L, then not-M. Premise 2. Not-K and M. Premise 3. Not-K
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