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