Consider the following premises. r. p_2 or ~p_4. r -> p_2. Can we infer ~p_2 from them?
 From r we can infer r or p_4. From p_2 or ~p_4 we can infer p_4 -> p_2. Finally, from r -> p_2, p_4 -> p_2, r or p_4 we can infer p_2, which contradicts ~p_2. Therefore, the answer is no.