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 3.4 - Page 144: 31


The reordering is: 4. If an animal is in the yard, then it is mine. 1. If an animal belongs to me, then I trust it. 5. If I trust an animal, then I admit it into my study. 3. If I admit an animal into my study, then it will beg when told to do so. 6. If an animal begs when told to do so, then that animal is a dog. 2. If an animal is a dog, then that animal gnaws bones. ∴ If an animal is in the yard, then that animal gnaws bones.

Work Step by Step

Universal transitivity: ∀x,P(x)→Q(x). ∀x,Q(x)→R(x). ∴∀x,P(x)→R(x).
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