Consider the following premises. p_8 <-> q. q_1 -> p_8. u -> q_1. Can we infer ~(u -> q) from them? If possible, name the inference rules being used at each step.
 From p_8 <-> q we can infer p_8 -> q via biconditional elimination. From u -> q_1, q_1 -> p_8 we can infer u -> p_8 via transitivity. Finally, from u -> p_8, p_8 -> q we can infer u -> q via transitivity, which contradicts ~(u -> q). Therefore, the answer is no.