Definition 1.1 (Sumset). Let $G$ be an abelian group. Given $A,B\subseteq G$, define the sumset $A+B$ to be

$$A+B:=\{a+b:a\in A,b\in B\}$$

and the difference set $A-B$ to be

$$A-B:=\{a+b:a\in A,b\in B\}.$$