hint
$\displaystyle A: \: 1,-1,1,-1,...$
$\displaystyle B: \: -1,1,-1,1,...$
But that depends upon how $\displaystyle AB$ is defined.
If it is defined by $\displaystyle AB=\left\{ {xy:x \in A\;\& \,y \in B} \right\}$ then $\displaystyle \sup(A)=\sup(AB)=\sup(B)$