Consider the following premises. q_11 <-> s. r -> q_11. q_11 -> r. Can we infer ~(r -> s) from them? If possible, name the inference rules being used at each step.
 From r -> q_11, q_11 -> r we can infer r <-> q_11 via biconditional introduction. From q_11 <-> s we can infer q_11 -> s via biconditional elimination. From r <-> q_11 we can infer r -> q_11 via biconditional elimination. Finally, from r -> q_11, q_11 -> s we can infer r -> s via transitivity, which contradicts ~(r -> s). Therefore, the answer is no.