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