Consider the following premises. ~u_4. p_1 -> u_4. q_3 <-> p_1. u -> q_3. Can we infer ~u from them? If possible, name the inference rules being used at each step.
 From p_1 -> u_4, ~u_4 we can infer ~p_1 via modus tollens. From q_3 <-> p_1 we can infer q_3 -> p_1 via biconditional elimination. From q_3 -> p_1, ~p_1 we can infer ~q_3 via modus tollens. Finally, from u -> q_3, ~q_3 we can infer ~u via modus tollens. Therefore, the answer is yes.