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# quiz 2 - CSE 260 Section 002 QUIZ-2 Propositional...

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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 q -p -q p->q -pVq -q->-p T T F F T T T T F F T F F F F T T F T T T F F T T T 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.

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q ( p ( q p )) q ( p ( ¬ q p )) implication law q (( p ∧ ¬ q ) ( p p )) distributes over q
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quiz 2 - CSE 260 Section 002 QUIZ-2 Propositional...

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