Discrete Mathematics with Applications 4th Edition

Published by Cengage Learning
ISBN 10: 0-49539-132-8
ISBN 13: 978-0-49539-132-6

Chapter 4 - Elementary Number Theory and Methods of Proof - Exercise Set 4.1 - Page 162: 45


This statement is false. As a counterexample, $3$ and $1$ are both odd, but $3-1=2$ and $2$ is even. Therefore, the difference of two odd integers is not necessarily odd.

Work Step by Step

The methods of this section allow us to show us the opposite: that an odd minus an odd is always even. In short, we have $(2m+1)-(2n+1)=2m+1-2n-1=2m-2n=2(m-n)$, where $2(m-n)$ is clearly even.
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