Consider the following premises. ~w. q_8 -> p_8. p_8 -> q_8. p_8 -> w. w -> p_8. Can we infer ~q_8 from them? If possible, name the inference rules being used at each step.
 From p_8 -> q_8, q_8 -> p_8 we can infer p_8 <-> q_8 via biconditional introduction. From p_8 -> w, w -> p_8 we can infer p_8 <-> w via biconditional introduction. From p_8 <-> w, ~w we can infer ~p_8 via biconditional elimination. Finally, from p_8 <-> q_8, ~p_8 we can infer ~q_8 via biconditional elimination. Therefore, the answer is yes.