Assignment:
Suppose that the number of men equals the number of women. Prove the following claims, or provide counterexamples:
(a) For every pair of matchings there exist preference relations for which these are two stable matchings.
(b) For every three matchings there exist preference relations for which these are three stable matchings.
(c) For every four matchings there exist preference relations for which these are four stable matchings.
Provide complete and step by step solution for the question and show calculations and use formulas.