Consider the following premises. r -> q_1. q_1 -> r. r -> q_1. Can we infer q_1 <-> r from them?
 From r -> q_1, q_1 -> r we can infer r <-> q_1. From r <-> q_1 we can infer q_1 -> r. Finally, from q_1 -> r, r -> q_1 we can infer q_1 <-> r. Therefore, the answer is yes.