Consider the following premises. q -> p_4. p_4 -> q. t_2 -> q. p_4 -> t. Can we infer ~(t_2 -> t) from them? If possible, name the inference rules being used at each step.
 From q -> p_4, p_4 -> q we can infer q <-> p_4 via biconditional introduction. From q <-> p_4 we can infer q -> p_4 via biconditional elimination. From q -> p_4, p_4 -> t we can infer q -> t via transitivity. Finally, from t_2 -> q, q -> t we can infer t_2 -> t via transitivity, which contradicts ~(t_2 -> t). Therefore, the answer is no.