For each of the three cases, try to see what $\lfloor 2x \rfloor$,  $\lfloor 2y \rfloor$, and $\lfloor x + y\rfloor$ are equal to in terms of $\lfloor x\rfloor$ and $\lfloor y \rfloor$. 

For example, when $\{x \}, \{y\} < \dfrac{1}{2}$, we have that $\lfloor 2x \rfloor = 2\lfloor x \rfloor$ since $2\{x\} < 1$, and $\lfloor x + y \rfloor = \lfloor x\rfloor + \lfloor y \rfloor$, since $\{x \} + \{y \} <1$.