Assignment:
Theorem is proved under the assumption that all preference relations are strict. Show by example that the theorem does not hold if there may be instances of indifference in the preference relations of the men and the women.
Theorem: Suppose that the number of men is greater than the number of women. If a particular man is not matched to any woman under some stable matching, then he is not matched to a woman under any stable matching.
Provide complete and step by step solution for the question and show calculations and use formulas.