Astable roommate problem with 4 students a, b, c, d is de ned as follows. each student ranks the other three in strict order of preference. a matching is de ned as the separation of the students into two disjoint pairs. a matching is stable if no two separated students prefer each other to their current roommates. does a stable matching always exist? if yes, give a proof. otherwise give an example roommate preference where no stable matching exists.