Assume the following preferences for men and women: nil: nt3. u,'3 > W4 7714: > mi > mi 1) 2) 3) [4 points] What is the matching produced by men-proposing DA algorithm? [3 points] What is the matching produced by women-proposing OA algorithm? [11 points] Find the set of all stable matchings and show that they form a lattice. [7 points] Show that women-proposing OA is not strategy-proof for this example: find how woman WI can misrepresent her preferences to get a better match.