1. Consider the following Marriage Problem with 5 women and 6 men (where s means "single"). Women's preferences: 2 3 4 5 6 6 2 2 1 4 4 2 3 3 4 5 i w - 6 Men's preferences: 2 3 4 5 w UnAWN- - N U 4 a) Determine the matching obtained by the Man-Proposing Deferred Acceptance procedure and determine the matching obtained by the Woman-Proposing Deferred Acceptance procedure. Display the steps. b) Verify that the man-optimal matching is weakly preferred by all men to the woman- optimal matching, and that the woman-optimal matching is weakly preferred by all women to the man-optimal matching. c) Is the man-optimal matching Pareto-dominated for all individuals? - for the men only? for the women only? Explain all your answers. d) Show that a man can manipulate the woman-optimal matching. c) Verify that the Rural Hospital Theorem holds for this