Consider the following premises. u_1 <-> q_9. u_1 <-> w. q <-> w. ~q_9. Can we infer q from them? If possible, name the inference rules being used at each step.
 From u_1 <-> q_9, ~q_9 we can infer ~u_1 via biconditional elimination. From u_1 <-> w, ~u_1 we can infer ~w via biconditional elimination. Finally, from q <-> w, ~w we can infer ~q via biconditional elimination, which contradicts q. Therefore, the answer is no.