Consider a set A = {a1, . . . , an} and a collection B1, . . . , Bm of subsets of A (i. e. Bi ⊆ A for each i.) We say that a set H ⊆ A is a hitting set for the collection B1, . . . , Bm if H contains at least one element from each Bi - that is, if H T Bi is not empty for each i (so H hits all the sets Bi .) We now define the hitting set problem as follows. We are given a set A = {a1, . . . , an}, a collection B1, . . . , Bm of subsets of A, and a number k. We are asked: Is there a hitting set H ⊆ A for B1, . . . , Bm so that the size of H is at most k? Prove that hitting set is NP-complete.