Consider the following premises. q -> q_8. p_2 -> q. ~p_8. p_8 <-> q_8. Can we infer p_2 from them? If possible, name the inference rules being used at each step.
 From p_8 <-> q_8, ~p_8 we can infer ~q_8 via biconditional elimination. From q -> q_8, ~q_8 we can infer ~q via modus tollens. Finally, from p_2 -> q, ~q we can infer ~p_2 via modus tollens, which contradicts p_2. Therefore, the answer is no.