Question 4 (6 marks) (Based on exercise 5.32 of DPU textbook) Suppose that n = 2k, where n and k are integers. Prove that there exists an instance of the set cover problem (Section 5.4 DPU textbook) with following properties. a) There are n elements in the base set. b) The optimal cover uses just two sets c) The greedy algorithm picks at least log n sets. Question 4 (6 marks) (Based on exercise 5.32 of DPU textbook) Suppose that n = 2k, where n and k are integers. Prove that there exists an instance of the set cover problem (Section 5.4 DPU textbook) with following properties. a) There are n elements in the base set. b) The optimal cover uses just two sets c) The greedy algorithm picks at least log n sets