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

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

(1) $\displaystyle P(A)=P(B)$ if and only if $\displaystyle P(A \cap B^c)=P(A^c \cap B)$

(2) Given $\displaystyle P(A)=0.5$ and $\displaystyle P(A \cup (B^c \cap C^c)^c)=0.8$, determine $\displaystyle P(A^c \cap (B \cup C))$

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 $\displaystyle P(A \cup B \cup C)=0.8$, am I right? What should I do?

Thanks a lot.