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# hw3 - CSCI-561 Fall 2010 Homework 3 Student name Macskassy...

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CSCI-561 Fall 2010 Macskassy Homework 3 Due Nov. 3, 2010 Student name: _____________________________ Student ID: _________________ Question 1 [Q1: 20 points] a). P Q is defined as being equivalent to (P Q) ^ (Q P). Based on this definition, show that P Q is logically equivalent to (P v Q) (P ^ Q). i) [5pts] By using truth tables. ii) [5pts] By using the following identities: ¬ (¬P) = P (P Q) = (¬P v Q) the contrapositive law: (P Q) = (¬Q ¬P) deMorgan's law: ¬ (P v Q) = (¬P ^ ¬Q) and ¬ (P ^ Q) = (¬P v ¬Q) the commutative laws: (P ^ Q) = (Q ^ P) and (P v Q) = (Q v P) the associative law: ((P ^ Q) ^ R) = (P ^ (Q ^ R)) the associative law: ((P v Q) v R) = (P v (Q v R)) the distributive law: P v (Q ^ R)) = (P v Q) ^ (P v R) the distributive law: P ^ (Q v R)) = (P ^ Q) v (P ^ R)

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CSCI-561 Fall 2010 Macskassy Homework 3 Due Nov. 3, 2010 Student name: _____________________________ Student ID: _________________ Question 1 (cont.) [Q1: 20 points] b) Consider the following propositional knowledge base: If April is whistling, then April is happy. If the house is clean, then April is happy. April is not happy. i ) Use PROPOSITIONAL RESOLUTION to prove that “the house is not clean and April is not whistling”. Use W =
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