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: 52

Answer

~(p ˅ ~q) ˅ (~p ˄ ~q) ≡ (~p˄q) ˅ (~p ˄ ~q) (By De Morgan’s laws) ≡ ~p ˄ (q ˅ ~q) (By Distributive laws) ≡ ~p ˄ t (By Negation laws) ≡ ~p (By Identity laws)

Work Step by Step

~(p ˅ ~q) ˅ (~p ˄ ~q) ≡ (~p˄q) ˅ (~p ˄ ~q) (By De Morgan’s laws) ≡ ~p ˄ (q ˅ ~q) (By Distributive laws) ≡ ~p ˄ t (By Negation laws) ≡ ~p (By Identity laws)
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