Q1) Set cover problem is as follows: given a set S of subsets S1, ..., Sm of universal set U={1, ..., n}, determine smallest subset of subsets T ⊂ S such that ∪ti∈T ti = U. For instance, there are the following subsets, S1 = {1, 3, 5}, S2 ={2, 4}, S3 = {1, 4}, and S4 = {2, 5} The set cover would then be S1 and S2. Determine a counterexample for the following algorithm based on greedy strategy: Choose the largest subset for cover, and then delete all its elements from universal set. Repeat by adding subset containing the largest number of uncovered elements until all are covered.