Answer
Yes, see explanations.
Work Step by Step
If x is an integer, we have $\lceil -x \rceil = -x = -\lfloor x \rfloor $ . If x is not an integer, let M and N be integers (positive or negative) and $ M\lt x \lt N $. Thus, we have $-N\lt -x \lt -M $, so $\lceil -x \rceil = -M $ and $-\lfloor x \rfloor=-M $
