Consider the following premises. ~t. w <-> t. q_3 or u_1. q_3 <-> w. Can we infer ~u_1 from them? If possible, name the inference rules being used at each step.
 From q_3 <-> w we can infer q_3 -> w via biconditional elimination. From w <-> t, ~t we can infer ~w via biconditional elimination. From q_3 -> w, ~w we can infer ~q_3 via modus tollens. Finally, from q_3 or u_1, ~q_3 we can infer u_1 via disjunctive syllogism, which contradicts ~u_1. Therefore, the answer is no.