Consider the following premises. p_2 -> w_4. q_8. w_4 -> ~q_8. p_2 or w. Can we infer ~w from them? If possible, name the inference rules being used at each step.
 From w_4 -> ~q_8, q_8 we can infer ~w_4 via modus tollens. From p_2 -> w_4, ~w_4 we can infer ~p_2 via modus tollens. Finally, from p_2 or w, ~p_2 we can infer w via disjunctive syllogism, which contradicts ~w. Therefore, the answer is no.