## Discrete Mathematics with Applications 4th Edition

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