Consider the following premises. q_2 -> u. u <-> q_4. ~q_2. q_2 or ~u. Can we infer ~q_4 from them? If possible, name the inference rules being used at each step.
 From q_2 or ~u we can infer u -> q_2 via rewriting. From u -> q_2, q_2 -> u we can infer u <-> q_2 via biconditional introduction. From u <-> q_2, ~q_2 we can infer ~u via biconditional elimination. From u <-> q_4 we can infer q_4 -> u via biconditional elimination. Finally, from q_4 -> u, ~u we can infer ~q_4 via modus tollens. Therefore, the answer is yes.