Problem $6$: Stable Marriage

Decide whether the following statement is true or false. If it is true, give a short proof. If it is

false, give a counter example. In every instance of the Stable Marriage problem, there is a stable

matching containing a pair $(m,w)$ such that $m$ is ranked first on the preference list of $w$ and $w$ is

ranked first on the preference list of $m.$

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