Discrete Mathematics

1) Let a, b, c, d be any integers. Prove that the product

(a b)(a c)(a d)(b c)(b d)(c d)

is divisible by 6.

For example, if a = 10, b = 6, c = 4, d = 8 then the product will be equal to 26880, and that is divisible by 6, because 26880 6 = 4480, remainder 0.

2) a) Give definitions for the set operations of union, intersection, and difference (please give definitions using set-builder notation. For example if I wanted to define the complement of a set I would define it this way: A = {x | (x A) }

b) Use your definitions to prove that for all sets A and B

(A B) (B A) = (A B) (A B)