Consider the following premises. p_15 -> w_1. t. w_1 -> ~t. ~p_15 -> q_3. w_1 -> p_15. Can we infer q_3 from them? If possible, name the inference rules being used at each step.
 From p_15 -> w_1, w_1 -> p_15 we can infer p_15 <-> w_1 via biconditional introduction. From w_1 -> ~t, t we can infer ~w_1 via modus tollens. From p_15 <-> w_1, ~w_1 we can infer ~p_15 via biconditional elimination. Finally, from ~p_15 -> q_3, ~p_15 we can infer q_3 via modus ponens. Therefore, the answer is yes.