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: 10

Answer

Truth table for (p $\rightarrow$ r) $\leftrightarrow$ (q $\rightarrow$ r):

Work Step by Step

First fill in the eight possible combinations of truth values for p, q, and r. Evaluate the if/then statements on either side of the biconditional, first (p $\rightarrow$ r), second (q $\rightarrow$ r). When the if element is T and then element is F, the statement is F. In all other cases the statement is T. Lastly evaluate (p $\rightarrow$ r) $\leftrightarrow$ (q $\rightarrow$ r) according to the definition of bioconditional (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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