Consider the following premises. r <-> s. s or ~q_2. Can we infer ~(q_2 -> r) from them? If possible, name the inference rules being used at each step.
 From s or ~q_2 we can infer q_2 -> s via rewriting. From r <-> s we can infer s -> r via biconditional elimination. Finally, from q_2 -> s, s -> r we can infer q_2 -> r via transitivity, which contradicts ~(q_2 -> r). Therefore, the answer is no.