Let m, m be two of the men and w, w be two of the women in an instance of the Stable Matching Problem with n men and n women. Assume m, M, W, W2's preference lists are: m's preference: W > W>.. m's preference: W2 > W >... w's preference: m > m > w's preference: m > m >... So, we only know the favorite and the second favorite of each of these four persons. (a) (10 pt) Show that if we run Gale-Shapley algorithm with men proposing, then m is matched to w and m is matched to w. (b) (10 pt) Show that in every stable matching, m, m are matched to w, W2, i.e., (m, W), (m, W) or (m, W2), (m2, W) must be part of any stable matching.