Consider the following premises. forall x: ~P_2(x). u_2 <-> P_2(a). Can we infer ~u_2 from them? If possible, name the inference rules being used at each step.
 From forall x: ~P_2(x) we can infer ~P_2(a) via universal instantiation. From u_2 <-> P_2(a) we can infer u_2 -> P_2(a) via biconditional elimination. Finally, from u_2 -> P_2(a), ~P_2(a) we can infer ~u_2 via modus tollens. Therefore, the answer is yes.