6. There are four schools (s1, 52, 53, s4), each with only one seat, and four students (i1, i2, i3, i4). Student preferences and school priorities are as follows: Student Preference il s2>s3>s5l1>s4 i2 s4>s52>51>53 i3 1>54>52>53 i4 s4>s52>53>51 School Priority sl i1>i3>i2>i4 52 i4>i2>i3>1i1 s3 i2>i3>i1>14 54 i3>i2>i1>i4 (a) (6 points) Find the matching under the Boston Mechanism (BM), assuming that students truthfully reveal their preferences. Show your steps. Is the resulting matching strategy proof? Explain. (b) (6 points) Find the matching under the Deferred Acceptance Mechanism (DA). Show your steps. (c) (6 points) Find the matching under the Top-Trading Cycle Mechanism (TTC). Show your steps. (d) (6 points) Is the matching under DA Pareto Optimal? Is the matching under TTC stable? Explain