Show that if $X= \emptyset$ and $r \in \mathbb{R}$ then $r\emptyset=\emptyset+r=\emptyset$.

Defitinions:

* $X+r=\{x+r:x\in X\}$,
* $rX=\{rx:x\in X\}$.

Can you hint me? I know I will use these defitions. Yet, how?