Consider the following premises. u_3 <-> q_3. q_3 or ~u_3. ~u_3. Can we infer ~q_3 from them? If possible, name the inference rules being used at each step.
 From u_3 <-> q_3 we can infer q_3 -> u_3 via biconditional elimination. From q_3 or ~u_3 we can infer u_3 -> q_3 via rewriting. From u_3 -> q_3, q_3 -> u_3 we can infer u_3 <-> q_3 via biconditional introduction. From u_3 <-> q_3 we can infer q_3 -> u_3 via biconditional elimination. Finally, from q_3 -> u_3, ~u_3 we can infer ~q_3 via modus tollens. Therefore, the answer is yes.