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: 13

Answer

Truth tables:

Work Step by Step

For 13a: First fill in the 4 possible combinations of truth values for p and q. Then fill in the column for ~p. Evaluate the if/then statement (p $\rightarrow$ q). When the if element is T and then element is F, the statement is F. In all other cases the statement is T. Then evaluate ~p $\lor$ q according to the definition of OR (a $\lor$ b is true when either a is true, or b is true, or both a and b are true; it is false only when both a and b are false). Notice that (p $\rightarrow$ q) and (~p $\lor$ q) always share the same truth values, so they are logically equivalent. For 13b. Evaluate ~(p $\rightarrow$ q) by taking the negation of the truth values of (p $\rightarrow$ q) from the truth table for 13a. Fill in the values for ~q, then evaluate p $\land$ ~q according to the definition of AND (a $\land$ b is true when, and only when both a and b are true).
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.