Consider the following premises. p_9 <-> q_1. ~q_1. p_9 <-> q_4. Can we infer ~q_4 from them? If possible, name the inference rules being used at each step.
 From p_9 <-> q_1, ~q_1 we can infer ~p_9 via biconditional elimination. From p_9 <-> q_4 we can infer q_4 -> p_9 via biconditional elimination. Finally, from q_4 -> p_9, ~p_9 we can infer ~q_4 via modus tollens. Therefore, the answer is yes.