Question: In the stable matching problem, If m is the first man on the woman w's preference list and w is the first woman on m's

In the stable matching problem,

In the stable matching problem, If m is the first man on

If m is the first man on the woman w's preference list and w is the first woman on m's preference list, does it have to be the case that m and w must be matched to each other in every stable matching? If m is the first man on the woman w's preference list and w is the first woman on m's preference list, does it have to be the case that m and w must be matched to each other in every stable matching

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