Assignment:
In Julius’s list of preferences, Agrippina appears first, Messalina appears second, and Cleopatra appears third. Suppose there is a stable matching under which Julius is matched to Agrippina, and that there is a stable matching under which Julius is matched to Cleopatra. Is there necessarily a stable matching under which Julius is matched to Messalina? Either prove this statement or provide a counterexample.
Provide complete and step by step solution for the question and show calculations and use formulas.