Two problems with set theory
Pardon the format--I've never really done this before and I've not ever touched LaTeX.
1) Let A,B be subsets of a metric space S such that B is open and cl(A) ^ B is nonempty, with ^ being the intersect, and cl(A) is the closure of A. Show that A ^ B is nonempty.
2) Let A,B be subsets of a metric space S. Show that A is open if and only if cl(A ^ cl(B)) = cl(A ^ B) for every B in S.
I honestly don't have a clue where to begin with #1, and for #2 I know that A is open if and only if A = int(A), its interior, but then that's it.
I'm not looking for a full solution of anything. I just want a shove in the right direction because I'm just lost. I drew a picture, but that's all I've managed.
Thanks for any help.