Question: More formally, consider the following decision problem: given n items (say a1, . . . an), given m subsets of these items S1, S2, .

More formally, consider the following decision problem: given n items (say a1, . . . an), given m subsets of these items S1, S2, . . . , Sm, and given an integer k, does there exist a set S of at most k items such that |S Si| 1 for all i {1, . . . , m}. Prove that this problem is in NP

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