Consider the following premises. p_2 -> p. ~p. Can we infer ~p_2 or u_3 from them? If possible, name the inference rules being used at each step.
 From p_2 -> p, ~p we can infer ~p_2 via modus tollens. Finally, from ~p_2 we can infer ~p_2 or u_3 via addition. Therefore, the answer is yes.