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: 26

Answer

$(P ∧ Q) ∨ Q≡ (P ∨ Q) ∧ Q $ are logically equall

Work Step by Step

The Boolean expression for (a) is (P ∧ Q) ∨ Q, and for (b) it is (P ∨ Q) ∧ Q. We must show that if these expressions are regarded as statement forms, then they are logically equivalent. But (P ∧ Q) ∨ Q ≡$ Q ∨ (P ∧ Q) $ by the commutative law for ∨ ≡ $(Q ∨ P) ∧ (Q ∨ Q)$ by the distributive law ≡ $(Q ∨ P) ∧ Q $ by the idempotent law ≡ $(P ∨ Q) ∧ Q$ by the commutative law for ∧ Following the circuit
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