Consider the following premises. w_4 -> q_8. w_4 or p_4. r_3 <-> q_8. ~r_3. Can we infer ~p_4 from them? If possible, name the inference rules being used at each step.
 From r_3 <-> q_8, ~r_3 we can infer ~q_8 via biconditional elimination. From w_4 -> q_8, ~q_8 we can infer ~w_4 via modus tollens. Finally, from w_4 or p_4, ~w_4 we can infer p_4 via disjunctive syllogism, which contradicts ~p_4. Therefore, the answer is no.