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 50: 48

Answer

a. ~(p∨~q)∨(r∨q) b. ~(~(~p∧q)∧(~r∧~q))

Work Step by Step

A. p∨~q → r∨q = ~(p∨~q)∨(r∨q) substitute using the equivalence p → q =∼p ∨ q with (p∨~q) = p and (r∨q) = p B. Using the form from part a ~(p∨~q)∨(r∨q) = ~(~(~p∧~(~q)))∨(r∨q) substitute using the equivalence p∨q=∼(∼p∧∼q) , with p = p and q = ~q =(~p∧q)∨(r∨q) Simplify double inversions =(~p∧q)∨~(~r∧~q) substitute using the equivalence p∨q=∼(∼p∧∼q) , with r = p and ~q = q =~(~(~p∧q)∧~(~(~r∧~q))) substitute using the equivalence p∨q=∼(∼p∧∼q) , with (~p∧q) = p and ~(~r∧~q) = q =~(~(~p∧q)∧(~r∧~q)) Simplifying double inversions
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.