Hi,

I am working through Bert Mendelson's "Introduction to Topology" and am having some trouble with proofs.

The text in well presented but to get a proper understanding I am working through the excercises. I am still on Chapter 1 which deals with sets and for the most part the excercises seem trivial to the point where its seems to me no proof is needed BUT there are a couple of questions that have me stumped (there are no worked solutions a problem with most maths books I find).

I would really apreciate it if somebody could walk me through a few proofs (it will probably take more than a couple before I get my head into gear), so here a couple of the excercises..

First one that seems trivial to me but one I am having trouble forming a proof for,

Let $\displaystyle A, B, D \subset S$

Prove $\displaystyle A \cap (B \cup D) = (A \cap B) \cup (A \cap D)$

Secondly not so trivial to my mind,

Let $\displaystyle \{A_\alpha\}_{\alpha\in I}$ be an indexed family of subsets of a set S. Let $\displaystyle J \subset I$

Prove $\displaystyle \bigcap_{\alpha\in J} A_\alpha \supset \bigcap_{\alpha\in I} A_\alpha$

Any help with this most apreciated.