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: 25

Answer

The inverse of p $\rightarrow$ q is ~p $\rightarrow$ ~q. The truth table shows the conditional statement is not logically equivalent to its inverse.
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Work Step by Step

To evaluate the if/then statements, recall by the definition of a conditional statement, when the if element is T and the then element is F, the statement is F. In all other cases the statement is T. 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. The truth table differs in rows 2 and 3. Hence the two statements are not logically equivalent.
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