Consider the following premises. u -> q_3. u -> q_3. q_3 <-> u. Can we infer ~(u <-> q_3) from them? If possible, name the inference rules being used at each step.
 From q_3 <-> u we can infer q_3 -> u via biconditional elimination. Finally, from u -> q_3, q_3 -> u we can infer u <-> q_3 via biconditional introduction, which contradicts ~(u <-> q_3). Therefore, the answer is no.