Discrete Mathematics with Applications 4th Edition

Published by Cengage Learning
ISBN 10: 0-49539-132-8
ISBN 13: 978-0-49539-132-6

Chapter 2 - The Logic of Compound Statements - Exercise Set 2.1 - Page 38: 51

Answer

p ∧ (∼q ∨ p) ≡ p ∧ (p ∨ ~q) (Commutative law) p ∧ (p ∨ ~q) ≡ p (Absorption Law)

Work Step by Step

Commutative law states p ∨ q ≡ q ∨ p and absorption law states p ∧ (p ∨ q) ≡ p so having ~q instead of q and applying the laws we get p ∧ (∼q ∨ p) ≡ p.
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