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 3.4 - Page 142: 2

Answer

The conclusion is: $\therefore$ 0 is even.

Work Step by Step

Universal modus ponens: $\forall x$, if $P(x)$ then $Q(x).$ $P(a)$ for a particular $a$. $\therefore Q(a)$. In this case P(x) is: If an integer x equals $2\cdot k$ and k is an integer. Q(x) is: x is even. a is 0 and k is 0. The conclusion Q(a) is: 0 is even.
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