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: 16

Answer

These two statements are not logically equivalent. Let p represent "you paid full price" and q represent "you didn't buy it at Crown Books." Hence "If you paid full price, you didn't buy it at Crown Books" has the form p $\rightarrow$ q, and "You didn't buy it at Crown Books or you paid full price" has the form q$\lor$p. These two statements differ in their truth values (see the truth table).
1506213470

Work Step by Step

To construct the truth table, first fill in the 4 combinations of truth values for p and q. Then evaluate p $\rightarrow$ q. Recall by the definition of a conditional statement, when the if element is T and then then element is F, the statement is F. In all other cases the statement is T. Lastly evaluate q$\lor$p by the definition of OR (q$\lor$ p is true when either q is true, or p is true, or both q and p are true; it is false only when both q and p are false). The two statements are only logically equivalent if, and only if, they have identical truth values for each possible substitution of statements for their statement variables.
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.