Show that if $\displaystyle \mathcal{B}$ is a basis for $\displaystyle X$ and $\displaystyle \mathcal{G}$ is a basis for $\displaystyle Y$, then $\displaystyle \mathcal{B} \times \mathcal{G} = \{B \times G|B \in \mathcal{B}, G \in \mathcal{G}\}$ is a basis for $\displaystyle X \times Y.$

Any help would be appreciated.