Consider the following premises. w -> q_4. w -> q_4. q_4 -> w. Can we infer ~(q_4 <-> w) from them? If possible, name the inference rules being used at each step.
 From w -> q_4, q_4 -> w we can infer w <-> q_4 via biconditional introduction. From w <-> q_4 we can infer q_4 -> w via biconditional elimination. Finally, from q_4 -> w, w -> q_4 we can infer q_4 <-> w via biconditional introduction, which contradicts ~(q_4 <-> w). Therefore, the answer is no.