Consider the following premises. p_1 -> q_1. q_1 -> q. ~q. Can we infer ~p_1 from them? If possible, name the inference rules being used at each step.
 From p_1 -> q_1, q_1 -> q we can infer p_1 -> q via transitivity. Finally, from p_1 -> q, ~q we can infer ~p_1 via modus tollens. Therefore, the answer is yes.