Consider the following premises. w. q_11 -> u. w -> q_11. q <-> u. Can we infer ~q from them? If possible, name the inference rules being used at each step.
 From w -> q_11, q_11 -> u we can infer w -> u via transitivity. From q <-> u we can infer u -> q via biconditional elimination. From w -> u, u -> q we can infer w -> q via transitivity. Finally, from w -> q, w we can infer q via modus ponens, which contradicts ~q. Therefore, the answer is no.