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: 33

Answer

2. If a bird is in this aviary, then it belongs to me. 4. If a bird belongs to me, then it is at least 9 feet high. 1. If a bird is at least 9 feet high, then it is an ostrich. 3. If a bird lives on mince pies, then it is not an ostrich. Contrapositive: If a bird is an ostrich, then it does not live on mince pies. ∴ If a bird is in this aviary, then it does not live on mince pies; that is, no bird in this aviary lives on mince pies.

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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