Assignment:
Consider a matching problem in which the preference relations of the men and women may include instances of indifference. Given a stable matching to such a matching problem, is it always possible to replace the weak preference relations (i.e., with instances of indifference) with strict preference relations in such a way that the stable matching with respect to the weak preference relations is also a stable matching with respect to the strict preference relations? If your answer is yes, prove it; if your answer is no, provide a counterexample.
Provide complete and step by step solution for the question and show calculations and use formulas.