ExSolution - 2200 x 2200 y(C(x P(y>S(x,y C 5 x 5...

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January 24 In-Class Exercise Solution Discussion
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Statement or Not? 1. The greatest common divisor (GCD) of 305 and 735 is 21. A. Yes B. No 1. It probably will rain today. A. Yes B. No
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Translate into symbolic notation Symbols A: Interest rates drop. B: The housing market improves. C: The federal discount rate drops. 1. If interest rates drop, the housing market will improve. A. A -> B B. B -> A 2. If either the federal discount rate doesn’t drop or the interest rates do not drop, the housing market will not improve. A. (A v B) -> C B. (A’ v B’) -> C’ C. (A v B)’ -> C’ D. (A’ B’) -> C’
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Predicate symbols and predicate wff Predicate symbols C(x): x is a Corvette; P(x): x is a Porsche; F(x): x is a Ferrari S(x,y): x is slower than y. Predicate wff Statement: If there is a Corvette that is slower than a Ferrari, then all Corvettes are slower than all Porsches. A: (C(x) -> S(x,F(x))) -> S(C(x), P(x)) B: ( 5 x)( 5 y)(C(x) F(y)->S(x,y)) -> (
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Unformatted text preview: 2200 x) ( 2200 y)(C(x) ∧ P(y)->S(x,y)) C: ( 5 x)( 5 y)(C(x) ∧ F(y) ∧ S(x,y)) -> ( 2200 x) ( 2200 y)(C(x) ∧ P(y)->S(x,y)) Negation • The network is slow or not functioning well.” A. The network is fast but not functioning well. B. The network is either fast or functioning well. C. The network is fast and functioning well. D. Other Negation • Every website either has text or video. A. Some website either has text or video. B. Every website has no text and no video. C. Some website has no text and no video. D. Some website has no text or no video. E. Other Proof – truth table 1. A ∨ (B ∧ A’) ⇔ A ∨ B A B A’ B ∧ A’ A v (B ∧ A’) AvB T T F F T T T F F F T T F T T T T T F F T F F F Proof Sequence • (C’ ∨ A) ∧ (A -> B) ∧ C -> B is a valid argument 1. C’ v A hyp. 2. A->B hyp. 3. C hyp. 4. C->A 1, imp 5. A 3,4,mp 6. B 5,2, mp-- The end....
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