1. Let A, B, C and D be sets. Determine whether the following statements are true or false. Prove the statements which are true; note that Venn Diagrams are not proofs.
Give a counter example for each statement which is false.
(a) If A ∩ B = A ∩ C, then B = C.
(b) If A ⊕ B = A ⊕ C, then B = C.
(c) If A 
B and B ⊆ C, then A C.
(d) A \ (B U C) = (A \ B) U (A \ C).
2. Let A, B and C be sets. Prove that if A ⊆ B and C 
D, then AxC Bx D.