Consider the following premises. u. q -> ~r. p_2. r. p_2 -> ~u. Can we infer q_10 and ~q 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. From q -> ~r, r we can infer ~q via modus tollens. From ~p_2 we can infer ~p_2 or q_10 via addition. From ~p_2 or q_10, p_2 we can infer q_10 via disjunctive syllogism. Finally, from q_10, ~q we can infer q_10 and ~q via conjunction. Therefore, the answer is yes. Notice, however, that the premises were contradictory, so we can infer anything from them.