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 13: 9

Answer

a) Sharks have not been spotted near the shore. b) Either swimming at the New Jersey shore is allowed, or sharks have been spotted near the shore. c) Swimming at the New Jersey shore is not allowed, and sharks have been spotted near the shore. d) If swimming at the New Jersey shore is allowed, sharks have not been spotted near the shore. e) If sharks have not been spotted near the shore, swimming at the New Jersey shore is allowed. f) If swimming at the New Jersey shore is not allowed, sharks have not been spotted near the shore. g) If swimming at the New Jersey shore is allowed, sharks have not been spotted near the shore, and if sharks have not been spotted near the shore, swimming at the shore is allowed. h) Either swimming at the New Jersey shore is not allowed, or both swimming at the New Jersey shore is allowed and sharks have not been spotted near the shore.

Work Step by Step

The most difficult part of this problem is to translate the logical structures into English sentences that make sense. Aside from that, the method of solving is substitution of the phrases into the compound propositions.
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