Is there necessarily a stable matching under which julius, Basic Statistics

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Is there necessarily a stable matching under which julius

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 counter example.

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