4. Given n men and n women in a marriage model where all potential mates are acceptable to each individual, prove that no man can be rejected by all n women in the Man-Proposing Deferred Acceptance procedure. 5. In a labour market with three hospitals, each with one position, a couple (1,2) and single doctor 3, the preferences are as follows: h1 hz h3 (1, 2) 2 (h1, h2) 2 (h2, hi ) h2 3 (h1, ha) h3 (1, 2) Determine whether there is a stable matching for this problem. N