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 2.4 - Page 77: 28

Answer

See below.

Work Step by Step

1. Based on the given conditions, we can convert each case as Boolean expressions: a) (P^Q)v(P∧~Q)v(∼P^~Q) b) P∨~Q 2. Use Theorem 2.1.1, we have: a) (P^Q)v(P∧~Q)v(∼P^~Q)≡((P^Q)v(P∧~Q))v(∼P^~Q)≡ P^(Qv~Q)v(∼P^~Q)≡P^(t)v(∼P^~Q)≡Pv(∼P^~Q)≡ (Pv∼P)^(Pv~Q)≡t^(Pv~Q)≡P∨~Q 3. Thus we can conclude that a) and b) are equivalent.
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