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The answer depends on whether you mean A intersecting (B union C) or (A intersecting B) union C.
Triple prime definition: Assume a<b<c. a, b, and c form a prime triple just if both the pairs (a, b) and (b, c) are twin primes.
The set A union B can be decomposed into three disjoint sub sets A\ (A int B), B\(A int B), and (A int B). So in this case (A union B) and (A int B) are fixed but "moving" elelments from A\ (A int B) into B\(A int B) will not affect (A union B) and (A int B). You should be able to fill in the details now.
b. 2x2x5 are prime factors
if we have set A and B consider A={1,2,3,4}and B={3,4,5,6} the union of these sets is A and B={1,2,3,4,5,6}and the intersection is{3,4} the union and the intersection are same only if A=B