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**Prove by mathematical induction that if A**

_{1}, A_{2}, ...., A_{n}and B are any n + 1 sets, then:Base step = n = 1 so P(1): A

_{1}∩ B = A

_{1}∩ B

Induction Step: LHS of P(k+1):

Substitute (k+1) for all N. Working LHS: (where {k U i = 1}A

_{i}is the union from 1 to n of A

_{k})

=(({k U i = 1}A

_{i}) U A

_{k+1}) ∩ B; then distribute:

=(({k U i = 1}(A

_{i} ∩ B) U ( A

_{k+1}∩ B)

then this is where I get stuck. I feel there is about one or two more steps but I can't seem to grasp it. Any suggestions?