A convex set is any set X where V931,502 e X and o: 6 (0,1), (19:1 + (1 0:)55'2 E X. Equivalently, a set X is convex if line segments connecting any 2 elements of X are always contained in X. Answer the questions below using the information from problem 1 about Mary and Brian's preferences. a. For Brian, is the set of all bundles that are weakly preferred to (b, m) = (9,0) convex? What if the set only includes strictly preferred bundles? b. For Brian, is the set of all bundles that are not weakly preferred to (b, m) = (9,0) convex? c. For Brian, is the set of all bundles that are weakly preferred and not strictly preferred to (b, m) = (9,0) convex? d. For Mary, is the set of all bundles that are weakly preferred to (b, m) = (10,10) convex? What if the set only includes strictly preferred bundles? e. For Mary, is the set of all bundles that are not weakly preferred to (b, m) = (10, 10) convex? f. For Mary, is the set of all bundles that are weakly preferred and not strictly preferred to (13,111) = (10,10) convex