Can anyone help me with these proofs:

1. Prove that for any set A and B, the

$\displaystyle P(A \cap B) = P(A) \cap P(B)$

where P(X) = power set of X.

2. Prove that for every real number x, there is a real number y such that

$\displaystyle (x+y = xy) \leftrightarrow x \neq 1$

3. Suppose F and G are nonempty family of sets and every element of F is disjoint from some element of G. Prove that the union of all sets in F and the intersection of all sets in G are disjoint.

THANKS! MY MATH 109 GRADE DEPENDS ON THIS!