Consider the following premises. p_1 -> s. s <-> w_3. q -> p_1. Can we infer ~(q -> w_3) from them? If possible, name the inference rules being used at each step.
 From s <-> w_3 we can infer s -> w_3 via biconditional elimination. From p_1 -> s, s -> w_3 we can infer p_1 -> w_3 via transitivity. Finally, from q -> p_1, p_1 -> w_3 we can infer q -> w_3 via transitivity, which contradicts ~(q -> w_3). Therefore, the answer is no.