Consider the following premises. r. t -> ~r. u -> t. ~u -> q_1. p. Can we infer p and q_1 from them? If possible, name the inference rules being used at each step.
 From t -> ~r, r we can infer ~t via modus tollens. From u -> t, ~t we can infer ~u via modus tollens. From ~u -> q_1, ~u we can infer q_1 via modus ponens. Finally, from p, q_1 we can infer p and q_1 via conjunction. Therefore, the answer is yes.