Consider the following premises. q -> P(a_7). forall y_4: P(y_4) <-> W(y_4). ~W(a_7). Can we infer ~q from them? If possible, name the inference rules being used at each step.
 From forall y_4: P(y_4) <-> W(y_4) we can infer P(a_7) <-> W(a_7) via universal instantiation. From P(a_7) <-> W(a_7), ~W(a_7) we can infer ~P(a_7) via biconditional elimination. Finally, from q -> P(a_7), ~P(a_7) we can infer ~q via modus tollens. Therefore, the answer is yes.