Discrete Mathematics and Its Applications, Seventh Edition

Published by McGraw-Hill Education
ISBN 10: 0073383090
ISBN 13: 978-0-07338-309-5

Chapter 1 - Section 1.3 - Propositional Equivalences - Exercises - Page 35: 31

Answer

Then (p _, q) _, r is false and p _, (q _, r) is true

Work Step by Step

To show that these are not logically equivalent. We need only find one assignment of truth values to p, q, and r for which the truth values of (p _, q) _, r and p _, (q _, r) differ. One such assignment is F for all three. Then (p _, q) _, r is false and p _, (q _, r) is true.
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