Consider the following premises. ~q_1. p_1 <-> q_3. p_1 -> q_1. Can we infer ~q_3 from them? If possible, name the inference rules being used at each step.
 From p_1 -> q_1, ~q_1 we can infer ~p_1 via modus tollens. Finally, from p_1 <-> q_3, ~p_1 we can infer ~q_3 via biconditional elimination. Therefore, the answer is yes.