Let U={u_(1),u_(2),dots,u_(n)} be a set. Consider we are given a collection of subsets S_(1),S_(2),dots,S_(m) of U. That is, S_(i)sube U for each 1 Let U={u1,u2,,un} be a set. Consider we are given a collection of subsets S1,S2,,Sm of U. That is, SiU for each 1im of the m subsets. We want to choose some of those m subsets so that the union of the chosen subsets is U. Set Cover Input: A set U={u1,u2,,un}, a collection of subsets S1,S2,,Sm of U, and an integer 0rm. Output: "Yes" if there exists a collection of at most r of the subsets Si whose union is U "No" otherwise. A set cover is a collection of subsets R1,R2,,R so that j=1Rj=U. This decision problem is thus called Set Cover. 1. Show that Set Cover Pm SAT