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 117: 38

Answer

True. The formal statement is: $\forall$ characters u, if u occurs in the sequence Discrete Mathematics, then u is lowercase. The negation is: $\exists$ at least one character u such that u occurs in Discrete Mathematics and u is not lowercase. The negation is false because Discrete Mathematics does not contain a character u. So the claim is vacuously true (or true by default).

Work Step by Step

A statement of the form $\forall x \in D$, if P(x) then Q(x) is called vacuously true or true by default if, and only if, P(x) is false for every x in D.
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