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 1.4 - Predicates and Quantifiers - Exercises - Page 53: 8

Answer

a) All rabbits hop. b) All animals are hopping rabbits. c) There exists an animal that, if it is a rabbit, then it hops. d) Some rabbits hop.

Work Step by Step

In predicate logic, $\forall$ means that the predicate applies to everyone in the domain, $\exists$ means that the predicate applies to at least one person in the domain, and $\neg$ means to negate what follows. Keeping this in mind, we formulate each of the sentences based upon the given formulas and the order in which the symbols appear.
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