The Set Cover problem is: Given a triple (X, S, k), where X is afinite set and S = {s1, s2, . . . , sn} is a collection of subsetsof X, and k is a positive integer, does there exist a subset C ⊆ Sof k sets whose union equals X. For example, if X = {1, 2, 3, 4, 5,6, 7, 8, 9}, s1 = {2, 4, 5}, s2 = {1, 4, 6}, s3 = {3, 7, 8}, s4 ={2, 7, 9}, s5 = {4, 6, 8}, s6 = {1, 3}, then X has a set cover ofsize 4 consisting of sets C = {s1, s5, s6, s4}.

Prove that the set cover problem is NP-complete. Give an exampleto illustrate your reduction and argue its correctness. Use VertexCover (VC) as the known NP-complete problem in your reduction.

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Answer to The Set Cover problem is: Given a triple (X, S, k), where X is a finite set and S = {s1, s2, . . . , sn} is a collection…