Let S and T be subsets of R. Prove the Following:

A) int(int S) = int S

for this one do I just need to take the set S, and show that the interiors interior is still part of the interior?

B) int(S $\displaystyle \cap$ T) = (int S) $\displaystyle \cap$ (int T)

For this one do I just assume there is some x $\displaystyle \in$ int(S $\displaystyle \cap$ T) and follow from there?