Answer
False.
Work Step by Step
False.
Counter example: let $x=1.1, y=-1.1$, we have
$LHS=\lfloor 1.1+1.1\rfloor =\lfloor 2.2\rfloor =2$
$RHS=\lfloor 1.1\rfloor - \lfloor -1.1\rfloor=1-(-2)=3\ne LHS$
You can help us out by revising, improving and updating this answer.
Update this answerAfter you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.