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