Mysteriously simple containment questions

[trap101]

Prove that the set i) S\subseteq S(Closure)
ii) (S^int)^int = S^int

Ok these supposedly simple containment questions irk me every time, how simplistic do I have to unravel the darn definitions:

Attempts: i) Let x \in S(Closure)
==> x\inS or x\in\partialS (Boundary of S)
==> if x\inS the there exists a B(r,x) \subseteq S
likewise if x\in\partialS then there exists the
B(r,x)\capS ≠∅ and B(r,x)\capS^c≠∅

==> S\subseteq S(Closure) I really don't see what else can be done



ii) isn't this just direct from the definition of the S^int? I mean it's the interior of an interior.

 

[verty]

i) First try to prove a simpler statement that is analogous to what you are asked to prove. For example, how would you prove that S⊆ S?

PS. This is all the help I can give here.