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Unformatted text preview: ANSWERS TO HW #1 Problems (from 1.1): 10, 28, 52, 60 10) a) r ⋀q, b) p ⋀ q ⋀ r, c) r → p, d) p ⋀ ¬ q ⋀ r, e) (p ⋀g) → r, f) r ↔ (q ⋁ p) 28) To construct the truth table for a compound proposition, we work from the inside out. For a & b, 1 st column for a, 2 nd column for b; p ¬G G → ¬G G ↔ ¬G T F F F F T T F For parts c and d, we have; p q G ∨ g G ∧ q G ⊕ (G ∨ ¡) (G ∧ q) → ( G ∨ g ) T T T T F T T F T F F T F T T F T T F F F F F T For part e; p q ¬G g → ¬G G ↔ g (g → ¬G) ↔ ( G ↔ g) T T F F T F T F F T F F F T T T F F F F T T T T For part f, p q ¬g G ↔ g (G → ¬g) ( G ↔ g) ⊕ (G ↔ ¬g) T T F T F T T F T F T T F T F F T T F F T T F T 52) The system is consistent. Let, L: The file system is licked, Q: New message will be queued N: The system is functioning normally B: new message will be sent to message buffer. Then the specification are, ¬¡ → ¢ , ¬¡ ↔ £ , ¬¢ → ¤ , ¬¡ → ¤ , and ¬¤ To have consistency, we must have B false so that...
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This document was uploaded on 10/16/2010.
 Spring '09

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