3 votes 3 votes Which of the following statements must be true? $\left \lfloor x \right \rfloor = \left \lceil x \right \rceil$ if and only if $x$ is an integer. $\left \lfloor x \right \rfloor + 1 = \left \lceil x \right \rceil$ if and only if $x$ is not an integer. $\left \lfloor x \right \rfloor \left \lceil y \right \rceil = \left \lceil x \right \rceil \left \lfloor y \right \rfloor$ for all $x,y.$ $-\left \lfloor x \right \rfloor = \left \lceil -x \right \rceil $ for all $x.$ Set Theory & Algebra goclasses2024-dm-2-weekly-quiz goclasses set-theory&algebra functions multiple-selects 1-mark + – GO Classes asked Apr 21, 2022 • retagged Apr 27, 2023 by Lakshman Bhaiya GO Classes 306 views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
4 votes 4 votes C is not true. Take $x = 2.5$ and $y = 4.$ Rest all are standard properties of floor and ceil functions. GO Classes answered Apr 21, 2022 GO Classes comment Share Follow See all 0 reply Please log in or register to add a comment.
