Hi I need help with the following:

1.

For any sets A and B, prove that:

a) A = (A ∩ B) or (A\B)

b) (A\B) or (B\A) = (A or B)\(A∩B)

2. For any sets A,B,C, prove that if

A\(B or C) = (A\B)or(A\C), then A∩(B or C) ⊆ A∩B∩C

3. For any sets A and B, prove that A\(A\B) = A∩B

4. Prove that if A\(B\C) ⊆ (A\B)\C then A∩C = 0

Any or all would be much appreciated!