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 3.3 - Page 129: 13

Answer

a. Statement: For every color, there is an animal of that color. There are animals of every color. b. Negation: ∃ a color C such that ∀ animals A, A is not colored C. For some color, there is no animal of that color.

Work Step by Step

Recall the negation of a multiply-quantified statement: ~($\forall x$ in D, $\exists y$ in E such that P(x,y)) $\equiv$ $\exists x$ in D such that $\forall y$ in E, ~P(x,y)
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