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: 43

Answer

If Jim does not do his homework regularly, then he will not pass the course. If Jim passes the course, then he did his homework regularly.

Work Step by Step

"r is a necessary condition for s" means "if not r, then not s". The contrapositive of p→q is ~q→~p. Let r = "Doing homework regularly" and s = "for Jim to pass the course". Then "if not r, then not s" would be "If Jim does not do his homework regularly, then he will not pass the course". Now that we have the If-Then statement, we can determine the contrapositive. The contrapositive is ~q→~p, which is "If Jim passes the course, then he did his homework regularly."
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