Consider the following premises. q -> w. w -> p_2. p_2 -> q. r -> w. Can we infer r -> p_2 from them?
 From p_2 -> q, q -> w we can infer p_2 -> w. From p_2 -> w, w -> p_2 we can infer p_2 <-> w. From p_2 <-> w we can infer w -> p_2. Finally, from r -> w, w -> p_2 we can infer r -> p_2. Therefore, the answer is yes.