Consider the following premises. s -> r_13. r_13 -> w_2. q -> s. q <-> w_2. Can we infer ~(q -> w_2) from them? If possible, name the inference rules being used at each step.
 From q -> s, s -> r_13 we can infer q -> r_13 via transitivity. Finally, from q -> r_13, r_13 -> w_2 we can infer q -> w_2 via transitivity, which contradicts ~(q -> w_2). Therefore, the answer is no.