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Unformatted text preview: CSE 260 Homework 4 Proofs: ANSWER It is due in class on Friday 1. (30 points) Section 1.5: 6, 28, 30 (10 points) Section 1.6: 26 2. ( 6 points) Show by using truth table that the following argument is not valid: It is raining and if it is raining it is cloudy and if it is not cloudy it is not humid logically implies it is not humid. r: It is raining c: It is cloudy h: It is humid !x denotes NOT x r c h r>c !c !h !c>!h r^(r>c)^(!c>!h) (r^(r>c)^(!c>!h))>!h T T T T F F T T F (r^(r>c)^(!c>!h))>!h cannot be a tautology. Therefore, the argument is not valid. 3. (20 points) Prove the resolution rule of inference (page 68 of the text), i.e., prove ( p ∨ q ) ∧ ( ¬ p ∨ r ) ⇒ ( q ∨ r ) (a) by means of truth table, p q r pvq !p !pvr (pvq)^(!pvr) qvr ((pvq)^(!pvr))>(qvr) T T T T F T T T T T T F T F F F T T T F T T F T T T T T F F T F F F F T F T T T T T T T T F T F T T T T T T F F T F T T F T T F F F F T T F F T (b) by means of derivation (hint: use implication law)....
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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.
 Spring '08
 SaktiPramanik

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