Consider the following premises. u -> r. r_8 <-> q_6. r_8 -> u. ~q_6. r -> r_8. Can we infer u from them? If possible, name the inference rules being used at each step.
 From u -> r, r -> r_8 we can infer u -> r_8 via transitivity. From r_8 <-> q_6, ~q_6 we can infer ~r_8 via biconditional elimination. From r_8 -> u, u -> r_8 we can infer r_8 <-> u via biconditional introduction. Finally, from r_8 <-> u, ~r_8 we can infer ~u via biconditional elimination, which contradicts u. Therefore, the answer is no.