An instance of the set cover problem consists of a set X of n elements, a family F of subsets of X, and an integer k. The question is, does there exist k subsets from F whose union is X? For example, if X = {1, 2, 3, 4} and F {{1, 2}, {2, 3}, {4}, {2, 4}}, there does not exist a solution for k = 2, but there does for k = 3 (for example, {1, 2}, {2, 3}, {4}). Prove that set cover is NP-complete with a reduction from vertex cover