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 3.2 - Page 116: 7

Answer

The statement is not existential. Informal negation: There is at least one order from store A for item B. Formal original statement: $\forall$ orders x, if x is from store A, then x is not for item B. Formal negation: $\exists$ an order x, such that x is from store A and x is for item B.

Work Step by Step

Recall the form of the negation of a universal conditional statement: $~(\forall x, P(x) \rightarrow Q(x)) \equiv \exists x$ such that $(P(x) \land $ ~$Q(x))$
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