Consider the following premises. s_2 -> s_3. s_3 <-> q. q -> s_2. Can we infer ~(s_2 <-> q) from them?
 From s_3 <-> q we can infer s_3 -> q. From s_2 -> s_3, s_3 -> q we can infer s_2 -> q. Finally, from s_2 -> q, q -> s_2 we can infer s_2 <-> q, which contradicts ~(s_2 <-> q). Therefore, the answer is no.