Consider the following premises. q. p_2 or ~u. p_2 -> ~q. Can we infer u from them? If possible, name the inference rules being used at each step.
 From p_2 or ~u we can infer u -> p_2 via rewriting. From p_2 -> ~q, q we can infer ~p_2 via modus tollens. Finally, from u -> p_2, ~p_2 we can infer ~u via modus tollens, which contradicts u. Therefore, the answer is no.