hw1 - 1. Every positive integer is smaller than the...

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CSE4/586 (Spring 2009): Homework 1 Due by Jan 27, in class. 1. (70 points) Let P , Q , R range over state predicates of some program. Prove or disprove the following: 1. [ P ( P Q ) P ] 2. [ P ( Q R ) ( P Q ) ( P R ) ] 3. [ P ( Q R ) ( P Q ) ( P R ) ] 4. [ ¬ ( P Q ) ≡ ¬ P ∨¬ Q ] (De Morgan) 5. [ ¬ ( P Q ) ≡ ¬ P ∧¬ Q ] (De Morgan) 6. [ P Q ≡ ¬ P Q ] 7. [ ( P n≡ Q ) ( Q n≡ P ) ] 2. (30 points) Translate the following English statements into predicate logic:
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Unformatted text preview: 1. Every positive integer is smaller than the absolute value of some negative integer. (Use abs.i for the absolute value of i ) 2. No integer is larger than all others. 3. There exists a village barber such that the population he shaves is the population of villagers that don’t shave themselves. (Russell’s Paradox) 1...
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