2. (42 points in total; 7 points each part) Doctors a, b, c, d and hospitals hy, h2 participate in a medical residency match with qr, = 2 and 92 = 1. Based on the submitted preferences, the Hospital-Proposing Deferred Acceptance mechanism yields matching 1 = a hi h2 hil Consider each question below separately, circle either "Yes" or "No," and justify your answers. A "Yes" or "No" by itself, or with the wrong explanation, is not worth any points. Given the information you have, is it possible that a) h2Pa hi, hiPc h2, and cPh, d? Yes No b) this matching is wasteful? Yes No c) h2 can manipulate this outcome? Yes No d) d is unmatched in a stable matching at the same preference profile? Yes No e) this matching is Pareto-efficient for the doctors? Yes No () c would rather be unmatched than matched to h2? Yes No