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 2.2 - Page 49: 9

Answer

Truth table for p $\land$ ~r $\leftrightarrow$ q $\lor$ r:

Work Step by Step

First fill in the eight possible combinations of truth values for p, q, and r. Then fill in ~r. Then fill in the column for p $\land$ ~r according to the definition of AND (p $\land$ ~r is true when, and only when, both p and ~r are true. If either p or ~r is false, or if both are false, p $\land$ ~r is false). Then fill in q $\lor$ r according to the definition of OR (q $\lor$ r is true when either q is true, or r is true, or both q and r and true; it is false only when both q and r are false). Then fill in the column for p $\land$ ~r $\leftrightarrow$ q $\lor$ r according to the definition of biconditional (a $\leftrightarrow$ b is true if both a and b have the same truth values and is false if a and b have opposite truth values).
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