This is the matching theory course

Please help with the second and thirs tasks

2. In what follows, we will prove the following lemma in two steps: Lemma 1 A matching ,u. is group stable {fund only {fit is (pairwise) stable. Proof of \"Only if" Direction. Suppose that a matching ,u. is pairwise stable, but also for contradiction that it [u] is not group stable. Then it is blocked by a coalition A and an outcome u'. a. [15 pts] Show that there exists at least one c E A. h. [15 pts] Show that there exists a students s E 01')_1{c) \\ (1401 (c) and a o E UJ}_1{S) \\{u'}_1[c) such that s >.; or.