Discrete Mathematics and Its Applications, Seventh Edition

Published by McGraw-Hill Education
ISBN 10: 0073383090
ISBN 13: 978-0-07338-309-5

Chapter 1 - Section 1.1 - Propositional Logic - Exercises - Page 15: 28

Answer

a) converse: if I ski tomorrow, it will snow today contrapositive: if it does not snow today, I will not ski tomorrow inverse: if I do not ski tomorrow, then it will not snow today b) converse: if it is a sunny summer day, then I go to the beach contrapositive: if I do not go to the beach, then it is not a sunny summer day inverse: if it is not a sunny summer day, then I do not go to the beach c) converse: if I need to sleep until noon, I stayed up late contrapositive: if I do not stay up late, I do not need to sleep until noon inverse: if I do not need to sleep until noon, then I did not stay up late

Work Step by Step

If a statement is "if p, then q," its: converse is "if q, then p", contrapositive is "if not p, then not q", and inverse is "if not q, then not p." For conditional statements a, b, and c, these statements are as follows: a) converse: if I ski tomorrow, it will snow today contrapositive: if it does not snow today, I will not ski tomorrow inverse: if I do not ski tomorrow, then it will not snow today b) converse: if it is a sunny summer day, then I go to the beach contrapositive: if I do not go to the beach, then it is not a sunny summer day inverse: if it is not a sunny summer day, then I do not go to the beach c) converse: if I need to sleep until noon, I stayed up late contrapositive: if I do not stay up late, I do not need to sleep until noon inverse: if I do not need to sleep until noon, then I did not stay up late
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