Consider the following premises. forall z_3: S(z_3) <-> Q_2(z_3). q. ~S(a_11). Can we infer ~Q_2(a_11) and q from them? If possible, name the inference rules being used at each step.
 From forall z_3: S(z_3) <-> Q_2(z_3) we can infer S(a_11) <-> Q_2(a_11) via universal instantiation. From S(a_11) <-> Q_2(a_11), ~S(a_11) we can infer ~Q_2(a_11) via biconditional elimination. Finally, from ~Q_2(a_11), q we can infer ~Q_2(a_11) and q via conjunction. Therefore, the answer is yes.