The binary operation * for combining sets is defined as A*B = (AÈB) - (AÇB).

Prove that G, consisting of the set of all subsets of a set S (including the empty set and the set S itself), together with the binary operation *, forms a group. You may assume that the associative property is satisfied.

Consider the set of all subsets of the natural numbers and solve the equation {1,2,4}*X = {3,4}.