Consider the following premises. q_2. q_2 <-> u_2. s -> q_2. u_2 -> s. Can we infer ~u_2 from them? If possible, name the inference rules being used at each step.
 From u_2 -> s, s -> q_2 we can infer u_2 -> q_2 via transitivity. From q_2 <-> u_2 we can infer q_2 -> u_2 via biconditional elimination. From u_2 -> q_2, q_2 -> u_2 we can infer u_2 <-> q_2 via biconditional introduction. From u_2 <-> q_2 we can infer q_2 -> u_2 via biconditional elimination. Finally, from q_2 -> u_2, q_2 we can infer u_2 via modus ponens, which contradicts ~u_2. Therefore, the answer is no.