Prove:

$\displaystyle R\circ (S\cap T)\subseteq R \circ S \cap R \circ T $

and an example where inclusion is strict

$\displaystyle R \circ S\cap T \subseteq R\circ (S\cap R^-^1 \circ T)$

and an example where inclusion is strict

I'm not understanding the composition of the intersection