Consider the following premises. p_4 -> w_2. w_2 -> q. q -> s_4. s_4 -> r_2. Can we infer p_4 -> r_2 from them? If possible, name the inference rules being used at each step.
 From p_4 -> w_2, w_2 -> q we can infer p_4 -> q via transitivity. From p_4 -> q, q -> s_4 we can infer p_4 -> s_4 via transitivity. Finally, from p_4 -> s_4, s_4 -> r_2 we can infer p_4 -> r_2 via transitivity. Therefore, the answer is yes.