Consider the following premises. q_8 -> q. p_2 <-> q_8. q -> p_2. Can we infer q <-> q_8 from them?
 From p_2 <-> q_8 we can infer p_2 -> q_8. From q -> p_2, p_2 -> q_8 we can infer q -> q_8. Finally, from q -> q_8, q_8 -> q we can infer q <-> q_8. Therefore, the answer is yes.