1. Consider the following set P of men's and women's preferences. Men Preferences Women Preferences A S T U V S D A B C B S V U T T A D C B C S U TV U C D B A D U V T S V A C D B (a) Find the stable matching for set P, that would be produced by running the Gale- Shapley algorithm as presented in class, in which the men do the proposing. (b) Set P has k different stable matchings. What is k? If you cannot determine k exactly, give the best upper bound and the best lower bound that you can. Justify your statement