Consider the following premises. p -> t. ~t_2. t_2 <-> t. p or q. Can we infer ~q from them? If possible, name the inference rules being used at each step.
 From t_2 <-> t we can infer t -> t_2 via biconditional elimination. From t -> t_2, ~t_2 we can infer ~t via modus tollens. From p -> t, ~t we can infer ~p via modus tollens. Finally, from p or q, ~p we can infer q via disjunctive syllogism, which contradicts ~q. Therefore, the answer is no.