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 1.2 - Applications of Propositional Logic - Exercises - Page 24: 40

Answer

a) $(\neg p \lor ¬ q)$ b) $\neg(p \lor ((¬ p) \land q))$

Work Step by Step

a) Starting from the left. First, the output of the top Not gate is : ¬ p The output of the bottom Not gate is: ¬ q. The output of the OR gate is ($\neg$ p $\lor$ ¬ q). Therefore the output of this circuit is $$(\neg p \lor ¬ q).$$ b) The output of the middle Not gate is: ¬ p. Then, the output of the bottom AND gate is: (¬ p) $\land$ q The output of the OR gate is: p $\lor$ ((¬ p) $\land$ q). Finally the output of the Not gate is: $$\neg(p \lor ((¬ p) \land q))$$
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.