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: 11

Answer

Truth table for (p $\rightarrow$ (q $\rightarrow$ r)) $\leftrightarrow$ ((p $\land$ q) $\rightarrow$ r):
1506203601

Work Step by Step

First fill in the eight possible combinations of truth values for p, q, and r. Then valuate the if/then statement (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. Next evaluate the if/then statement (p $\rightarrow$ (q $\rightarrow$ r)). Then evaluate the statement (p $\land$ q) according to the definition of AND (p $\land$ q is true when, and only when, both p and q are true. If either p or q is false, or if both are false, p $\land$ q is false). Next evaluate the if/then statement ((p $\land$ q) $\rightarrow$ r). Lastly evaluate the biconditional statement 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).
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.