This is all about open sets.
The interior of a set is an open set: it is the union of open sets.
So surely
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 T) = (int S) (int T)
For this one do I just assume there is some x int(S T) and follow from there?