Consider the following premises. r -> w. s -> s_1. s_1 -> r. s <-> w. Can we infer ~(r <-> s) from them? If possible, name the inference rules being used at each step.
 From s <-> w we can infer w -> s via biconditional elimination. From s -> s_1, s_1 -> r we can infer s -> r via transitivity. From r -> w, w -> s we can infer r -> s via transitivity. Finally, from r -> s, s -> r we can infer r <-> s via biconditional introduction, which contradicts ~(r <-> s). Therefore, the answer is no.