Consider the following premises. q_3 -> r_4. r_4 -> q. q <-> q_3. Can we infer ~(q_3 <-> r_4) from them?
 From q <-> q_3 we can infer q -> q_3. From r_4 -> q, q -> q_3 we can infer r_4 -> q_3. Finally, from q_3 -> r_4, r_4 -> q_3 we can infer q_3 <-> r_4, which contradicts ~(q_3 <-> r_4). Therefore, the answer is no.