Consider the following premises. u <-> q_8. u <-> q_4. Can we infer ~(q_4 -> q_8) from them? If possible, name the inference rules being used at each step.
 From u <-> q_8 we can infer u -> q_8 via biconditional elimination. From u <-> q_4 we can infer q_4 -> u via biconditional elimination. Finally, from q_4 -> u, u -> q_8 we can infer q_4 -> q_8 via transitivity, which contradicts ~(q_4 -> q_8). Therefore, the answer is no.