Consider the following premises. ~w. w <-> q_8. p_1 -> q_8. p_1 <-> u. Can we infer ~u from them? If possible, name the inference rules being used at each step.
 From w <-> q_8, ~w we can infer ~q_8 via biconditional elimination. From p_1 -> q_8, ~q_8 we can infer ~p_1 via modus tollens. Finally, from p_1 <-> u, ~p_1 we can infer ~u via biconditional elimination. Therefore, the answer is yes.