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: 28

Answer

Let p represent "I say it" and q represent "I mean it," then "I say what I mean" can be rewritten as, "if I say it, then I mean it," which is of the form p $\rightarrow$ q. The sentence "I mean what I say" can be rewritten as, "if I mean it, then I say it," which has the form q $\rightarrow$ p. Hence these two sentences are converses of each other. As was proven in problem 24, a conditional statement and its converse are not logically equivalent, so the Hatter is right.

Work Step by Step

The converse of the conditional statement p $\rightarrow$ q is q $\rightarrow$ p.
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.