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