Consider the following premises. w -> p_8. ~w. q_8 -> w. p_8 -> q_8. Can we infer p_8 from them? If possible, name the inference rules being used at each step.
 From p_8 -> q_8, q_8 -> w we can infer p_8 -> w via transitivity. From p_8 -> w, w -> p_8 we can infer p_8 <-> w via biconditional introduction. From p_8 <-> w we can infer p_8 -> w via biconditional elimination. Finally, from p_8 -> w, ~w we can infer ~p_8 via modus tollens, which contradicts p_8. Therefore, the answer is no.