Discrete Mathematics and Its Applications, Seventh Edition

Published by McGraw-Hill Education
ISBN 10: 0073383090
ISBN 13: 978-0-07338-309-5

Chapter 1 - Section 1.7 - Introduction to Proofs - Exercises - Page 91: 14

Answer

Proof below.

Work Step by Step

This is a direct proof. Let $x$ be a rational number expressed as the fraction $\frac{a}{b}$, with $a, b$ integers. Now, consider $1/x$. This is defined, because $x\neq 0$. $1/x=\frac{b}{a}$. Because $a, b\in \mathbb{Z}$, $1/x$ is rational.
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