# hw4 new - Sec 1.5 6 p it rains q it is foggy r the sailing...

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Unformatted text preview: Sec 1.5 6. p: it rains q: it is foggy r: the sailing race is held s: lifesaving demonstration will go on t: the trophy will be awarded H1: ( ¬p ¬q) ˅ ( r s) ˄ H2: r t H3: ¬t p 1. ¬t Hypothesis H3 2. r t Hypothesis H2 3. ¬r Modus tollens using (1) and (2) 4. ( ¬p ¬q) ˅ ( r s) ˄ Hypothesis H1 5. ( ¬p ¬q) ˅ r Simplification (4) 6. ¬( p q) ˄ r De Morgan’s Laws 7. p q ˄ Modus tollens using (3) and (6) 8. p Simplification (7) 28. 1. ∀ x ((¬P(x) Q(x)) ˄ R(x)) premise 2. (¬P(a) Q(a)) ˄ R(a) Universal Instantiation using 1 3. ¬P(a) R(a) Simplification using 2 4. P(a) R(a) ˅ Implication laws 5. ¬(¬R(a) P(a)) ˅ Double complement Law 6. ¬R(a) P(a) Implication laws 7. ∀ x(¬R(x) P(x)) Universal generalization using 6 30. Use resolution to show the hypotheses “Allen is a bad boy or Hillary is a good girl” and “Allen is a good boy or David is happy” imply the conclusion “Hillary is a good girl or David is Happy.”is a good boy or David is happy” imply the conclusion “Hillary is a good girl or David is Happy....
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## This note was uploaded on 01/29/2012 for the course CSE 260 taught by Professor Saktipramanik during the Spring '08 term at Michigan State University.

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hw4 new - Sec 1.5 6 p it rains q it is foggy r the sailing...

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