Discrete Mathematics with Applications 4th Edition

Published by Cengage Learning
ISBN 10: 0-49539-132-8
ISBN 13: 978-0-49539-132-6

Chapter 3 - The Logic of Quantified Statements - Exercise Set 3.2 - Page 117: 32

Answer

Statement: If the square of an integer is odd, then the integer is odd. Contrapositive: If an integer is not odd, then the square of the integer is not odd. Converse: If an integer is odd, then the square of the integer is odd. Inverse: If the square of an integer is not odd, then the integer is not odd. All the statements are true.

Work Step by Step

A statement of the form: $\forall x \in D$, if P(x) then Q(x), has as its contrapositive statement: $\forall x \in D$, if ~Q(x) then ~P(x), as its converse statement: $\forall x \in D$, if Q(x) then P(x), and as its inverse statement: $\forall x \in D$, if ~P(x) then ~Q(x).
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