I have a good idea of how to prove the following statements, I'm just wondering if they are correct.

Basically, letting S = Q x Q (where Q is the set of rational numbers, so S is therefore the Cartesian Product of the set of rational numbers). I've deduced that:

Boundary((Int(S)) = 0

Interior(Complement(S)) = R^2

Boundary(Int(Complement(S))) = 0

Closure(Interior(S)) = 0

Interior(Closure(S)) = R^2

So just need to make sure Im looking at these the right way, and these are correct statements.

Thanks a lot for your help.