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Unformatted text preview: CSE 260 - Section 002 QUIZ-2 Propositional equivalences- ANSWER (20 minutes)
NAME: 1. (10 points) Answer the following true/false. (a) p p p TRUE (b) Negation of the following statement: "James is young and strong" is "Either James is not young or James is not strong or both not strong and not you ng" TRUE (c) p p is a tautology TRUE (d) , form a functionally complete collection of logical operators. TRUE 2. (10 points) Use truth tables to verify that the following three compound propositions are equivalent: p q, p q, and q p (contrapositive) p T T F F q T F T F -p F F T T -q F T F T p->q T F T T -pVq T F T T -q->-p T F T T p q, p q and q p are equivalent because the corresponding row values in the three columns for the compound propositions are the same. 3. (10 points) Show by using the rules of logical equivalences that q (p q) and q p are logically equivalent. q (p (q p)) q (p (q p)) q ((p q) (p p)) q ((p q) p) (q (p q)) p (q p) (q q) p ((q p) T) p (q p) p q (p p) qp implication law distributes over is idempotent is associative distributes over tautology T is the identity for is associative is idempotent Laws are given below 1. Identity Laws pT p pF p 2. Double negation law (p) p 3. Negation Laws p p T p p F 4. Distributive laws p (q r) (p q) (p r) p (q r) (p q) (p r) 5. Associative laws (p q) r p (q r) (p q) r p (q r) 6. De Morgan's laws (p q) p q (p q) p q 7. Implication law p q p q ...
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This note was uploaded on 03/30/2008 for the course CSE 260 taught by Professor Saktipramanik during the Spring '08 term at Michigan State University.
- Spring '08