Consider the following premises. p_3 -> u_1. w. u_1 -> ~w. Can we infer ~p_3 or p_4 from them? If possible, name the inference rules being used at each step.
 From u_1 -> ~w, w we can infer ~u_1 via modus tollens. From p_3 -> u_1, ~u_1 we can infer ~p_3 via modus tollens. Finally, from ~p_3 we can infer ~p_3 or p_4 via addition. Therefore, the answer is yes.