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: 28

Answer

The logical connective $\leftrightarrow$, or "if and only if" evaluates to true if the propositions on each side of the connective have the same truth value. In the case of both $\neg p\leftrightarrow \neg q$ and $p\leftrightarrow q$, both $p$ and $q$ would have to be false, or both $p$ and $q$ would have to be true in order for the propositions on each side of the arrow to have the truth value. This means that the propositions evaluate to the same truth values for all values of $p$ and $q$, and so they are equivalent.

Work Step by Step

This question asked us for an explanation, so I included the full explanation in the answer section. Please see above.
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.