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: 16

Answer

a. There exists a real number u such that for all real numbers v, uv=v. There is a real number whose product with another real number is always equal to the other real number. b. negation: $\forall$ real numbers u, $\exists$ a real number v, such that uv $\neq$ v. For all real numbers u, there is a real number v, such that uv $\neq$ v.

Work Step by Step

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