Consider the following premises. q -> p_8. p_8 <-> w. w -> q. Can we infer ~(w <-> q) from them?
 From p_8 <-> w we can infer p_8 -> w. From q -> p_8, p_8 -> w we can infer q -> w. Finally, from w -> q, q -> w we can infer w <-> q, which contradicts ~(w <-> q). Therefore, the answer is no.