Consider the following premises. u_2 -> s. s -> u_2. q_8 -> u_2. s -> q_8. Can we infer ~(u_2 <-> s) from them? If possible, name the inference rules being used at each step.
 From s -> q_8, q_8 -> u_2 we can infer s -> u_2 via transitivity. From s -> u_2, u_2 -> s we can infer s <-> u_2 via biconditional introduction. From s <-> u_2 we can infer u_2 -> s via biconditional elimination. Finally, from u_2 -> s, s -> u_2 we can infer u_2 <-> s via biconditional introduction, which contradicts ~(u_2 <-> s). Therefore, the answer is no.