Consider the following premises. ~t. p_2 or s. s -> t. Can we infer p_2 from them? If possible, name the inference rules being used at each step.
 From s -> t, ~t we can infer ~s via modus tollens. From p_2 or s we can infer ~s -> p_2 via rewriting. Finally, from ~s -> p_2, ~s we can infer p_2 via modus ponens. Therefore, the answer is yes.