Consider the following premises. s -> r_1. s <-> r_2. r_1 -> r_2. Can we infer r_2 <-> r_1 from them?
 From s <-> r_2 we can infer r_2 -> s. From r_2 -> s, s -> r_1 we can infer r_2 -> r_1. Finally, from r_2 -> r_1, r_1 -> r_2 we can infer r_2 <-> r_1. Therefore, the answer is yes.