Consider the following premises. q_5 -> p_5. ~p_5. p_5 <-> q_5. Can we infer q_5 from them? If possible, name the inference rules being used at each step.
 From p_5 <-> q_5 we can infer p_5 -> q_5 via biconditional elimination. From p_5 -> q_5, q_5 -> p_5 we can infer p_5 <-> q_5 via biconditional introduction. Finally, from p_5 <-> q_5, ~p_5 we can infer ~q_5 via biconditional elimination, which contradicts q_5. Therefore, the answer is no.