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 143: 17

Answer

Invalid by converse error.

Work Step by Step

Converse Error: $\forall x$ if $P(x)$ then $Q(x)$. $Q(a)$ for a particular $a$. $\therefore P(a)$. (invalid conclusion) In this case P(x) is: an infinite series x converges. Q(x) is: the terms of the infinite series x go to 0. a is the infinite series $\sum_{n=1}^{\infty} \frac{1}{n}$.
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