3. Consider a particular solution for the Stable Marriage Problem with n men and n women.

(a) Suppose there is at least one man did not get his top choice and further suppose that this man has changed his mind: he now finds his wife to be more compatible than expected. In other words, suppose this man changes his preference list by moving his wife higher on the list. Does this change the stability of the marriages? Either prove the marriages remain stable or give an example to show that they dont.

(b) What if instead, there is some man who moves his wife lower on his preference list. Does this change the stability of the marriages? Either prove the marriages remain stable or give an example to show that they dont.