[8 Pts] Define predicates and prove the following using two-column proofs and the appropriate rules of inference: (a) (4 Pts) Jim, a student in class, owns a personal computer. Everyone who owns a personal computer types up their homework. Therefore, someone in class types up their homework. (b) (4 Pts) There are college towns in the midwest. All college towns are fun places to live. There is a town in the midwest that is a fun to live in