Consider the following premises. q. t -> ~q. t <-> p. p. Can we infer p_1 from them? If possible, name the inference rules being used at each step.
 From t -> ~q, q we can infer ~t via modus tollens. From t <-> p, ~t we can infer ~p via biconditional elimination. From ~p we can infer ~p or p_1 via addition. Finally, from ~p or p_1, p we can infer p_1 via disjunctive syllogism. Therefore, the answer is yes. Notice, however, that the premises were contradictory, so we can infer anything from them.