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