Consider a stable marriage/matching problem. Suppose that:

1. There are two men m1 and m2 and two women w1 and w2 and they have their own preference lists

2. The matching between m1-w1 and m2-w2 is stable.

Claim: m1-w2 and m2-w1 never be stable for this scenario.

Prove that this claim is correct no matter what the preferences of the men and women are as long as m1-w1 and m2-w2 is stable.

Else prove that this claim is incorrect using a counterexample for the preference lists of every man and woman and that for these preference lists m1-w1 and m2-w2 as well as m1-w2 and m2-w1 are stable.