Consider the following premises. w <-> p_2. p_2 <-> q. w -> u. ~u. Can we infer q from them? If possible, name the inference rules being used at each step.
 From w -> u, ~u we can infer ~w via modus tollens. From w <-> p_2, ~w we can infer ~p_2 via biconditional elimination. Finally, from p_2 <-> q, ~p_2 we can infer ~q via biconditional elimination, which contradicts q. Therefore, the answer is no.