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: 20


False. For example, taking $x=y=1.5$, we get $\lceil 1.5 \cdot 1.5\rceil=\lceil2.25\rceil=3$, but $\lceil1.5\rceil\cdot\lceil1.5\rceil=2\cdot2=4$.

Work Step by Step

Note that all the theorems involving the floor functions are analogous to ones involving ceiling functions. For example, this disproof is very similar to the one given in exercise 16, which has the more general form $\lfloor x\cdot y\rfloor\neq\lfloor x\rfloor\cdot\lfloor y\rfloor$.
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