We looked at a greedy algorithm to solve the set cover problem, and proved that if the optimal set cover has size k, then our greedy algorithm will find a set cover of size at most k loge n. here is a generalization of the set cover problem. • input: a set of elements b of size n; sets ; sm b; positive weights wi; . • output: a selection of the sets si whose union is b. • cost: the sum of the weights wi for the sets that were picked. design an algorithm to find the set cover with approximately the smallest cost. prove that if there is a solution with cost k, then your algorithm will find a solution with cost o(k logn).