Consider a set A = {a1,..., an} and a collectionB1,B2, ...,Bm of subsets of A (i.e., Bt c A for each i).
We say that a set H c A is a hitting set for the collectionB1,B2, ...,Bm if H contains at least one element from each Bi—that is, if H n Bt 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, B2,Bm of subsets of A, and a number k. We are asked: Is there a hitting set H ⊆ A for B1, B2,..., Bm so that the size of H is at most k?
Prove that Hitting Set is NP-complete.
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