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 4.5 - Page 197: 21

Answer

See below.

Work Step by Step

For any odd integer $n$, we can write $n=2k+1$ where $k$ is an integer. We have: $\lceil \frac{n}{2}\rceil =\lceil \frac{2k+1}{2}\rceil=\lceil k+\frac{1}{2}\rceil=k+1=\frac{n-1}{2}+1=\frac{n+1}{2}$
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