Consider the following premises. q. p_8 -> ~q. p_2 or p_8. Can we infer p_2 from them?
 From p_8 -> ~q, q we can infer ~p_8. From p_2 or p_8 we can infer ~p_8 -> p_2. Finally, from ~p_8 -> p_2, ~p_8 we can infer p_2. Therefore, the answer is yes.