Consider the following premises. w -> q_10. w <-> q_10. q_10 -> w. Can we infer ~(q_10 <-> w) from them?
 From w <-> q_10 we can infer w -> q_10. Finally, from q_10 -> w, w -> q_10 we can infer q_10 <-> w, which contradicts ~(q_10 <-> w). Therefore, the answer is no.