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