I would just like clarification for the following problem: Suppose $M_1$ and $M_2$ are two stable matchings between n men and n women, and we allow each woman to choose between the man she is paired with in $M_1$ and the partner she receives in $M_2$. Each woman always chooses the man she prefers. Show that the result is a stable matching between the men and the women.
Clarification: I understand what it means to be a stable marriage. However, I do not know what exactly $M_1$ and $M_2$ are. Are they just the two different lists each man and woman provides, which order their preferences for each man and each woman? Furthermore, what are the differences between the words "paired" and "received" as it pertains to this problem? I appreciate the input.