Consider the following premises. r_8 -> w. p_4 -> r_8. w -> q. q -> p_4. Can we infer ~(r_8 -> q) from them? If possible, name the inference rules being used at each step.
 From q -> p_4, p_4 -> r_8 we can infer q -> r_8 via transitivity. Finally, from r_8 -> w, w -> q we can infer r_8 -> q via transitivity, which contradicts ~(r_8 -> q). Therefore, the answer is no.