Consider the following premises. t_1. p_10 -> ~q_10. q_10. t_1 -> p_10. Can we infer u_2 from them? If possible, name the inference rules being used at each step.
 From p_10 -> ~q_10, q_10 we can infer ~p_10 via modus tollens. From t_1 -> p_10, ~p_10 we can infer ~t_1 via modus tollens. From t_1 we can infer t_1 or u_2 via addition. Finally, from t_1 or u_2, ~t_1 we can infer u_2 via disjunctive syllogism. Therefore, the answer is yes. Notice, however, that the premises were contradictory, so we can infer anything from them.