Consider the following “tricky” set cover problem. Let E = {1, 2, ... , p} where p = 2k+1 − 2 for some k > 0. Let TE = {S1,S2, ... ,Sk,X,Y}, be such that (a) Si and Sj are disjoint for all 1 ≤ (i, j) ≤ k, i = j, (b) Si contains 2i elements, (c) S1 ∪S2 ∪ ... ∪Sk = E, and (d) X contains half the elements from each Si and Y contains the remaining half. Thus X ∩ Y = Ø and X ∪ Y = E. The problem is to find the minimal set cover of E. For example, for k = 2 we have E = {1, 2, 3, 4, 5, 6}, TE = {S1,S2,X,Y}, S1 = {1, 2},S2 = {3, 4, 5, 6}, X = {1, 3, 4}, and Y = {2, 5, 6}. The minimal cover for this problem is {X,Y}. Show that both the greedy and the CMIMX algorithms fail to compute the minimal cover.