Hi, can anyone please help me with this question? Thanks a lot.

Let A, B, and C be any three events. Show that:

(1) if and only if

(2) Given and , determine

For first part, I don't know how to start at all. Plus, with "if and only if", does that mean I need to prove from two directions?

For second part, I did draw Venn Diagram, but still don't feel that is very helpful, except I did find , am I right? What should I do?

Thanks a lot.