True or False:

If $\displaystyle R$ is a noetherian ring and if $\displaystyle A$ and $\displaystyle B$ are subsets of $\displaystyle R$, then the intersection $\displaystyle <A>\cap<B>$, of the ideals they generate is generated by a finite subset of $\displaystyle A\cap B$

A hint would preferred to the full solution, I just don't know how to start this, thanks.