Consider the following premises. t_3 -> ~r. r. p_1 <-> q. p_1 -> t_3. Can we infer q from them? If possible, name the inference rules being used at each step.
 From t_3 -> ~r, r we can infer ~t_3 via modus tollens. From p_1 -> t_3, ~t_3 we can infer ~p_1 via modus tollens. Finally, from p_1 <-> q, ~p_1 we can infer ~q via biconditional elimination, which contradicts q. Therefore, the answer is no.