[Solved]6 Prove Following Problem Np Complete Given Positive Integers K N List Sets S1 S2 Sm 1 2 Q37275967

6. Prove that the following problem is NP-Complete. Given positive integers k, n and a list of sets S1, S2,… , Sm 1,2, ., n). decide if there exists a set CC 1,2,…, m such that l Cl = k and Sîn Sj = 0 for all i, j E C with J. 8. Recall the definition of Vertex-Cover = {(G, k): G is a graph that has a vertex cover of size k} Assume that Vertex-Cover is in P. Give a polynomial-time Turing Machine which, given a graph G and an integer k as input, will halt and output a vertex cover of G of size at most k-that is, it halts with the encoding of an actual vertex cover on its tape. Show transcribed image text 6. Prove that the following problem is NP-Complete. Given positive integers k, n and a list of sets S1, S2,… , Sm 1,2, ., n). decide if there exists a set CC 1,2,…, m such that l Cl = k and Sîn Sj = 0 for all i, j E C with J. 8. Recall the definition of Vertex-Cover = {(G, k): G is a graph that has a vertex cover of size k} Assume that Vertex-Cover is in P. Give a polynomial-time Turing Machine which, given a graph G and an integer k as input, will halt and output a vertex cover of G of size at most k-that is, it halts with the encoding of an actual vertex cover on its tape.

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Answer to 6. Prove that the following problem is NP-Complete. Given positive integers k, n and a list of sets S1, S2,… , Sm 1,2,… . . .