Consider the following premises. ~r_4 -> q. w. r_4 -> ~w. Can we infer ~q from them? If possible, name the inference rules being used at each step.
 From r_4 -> ~w, w we can infer ~r_4 via modus tollens. Finally, from ~r_4 -> q, ~r_4 we can infer q via modus ponens, which contradicts ~q. Therefore, the answer is no.