Consider the following premises. q <-> q_8. q <-> q_4. Can we infer ~(q_4 -> q_8) from them? If possible, name the inference rules being used at each step.
 From q <-> q_8 we can infer q -> q_8 via biconditional elimination. From q <-> q_4 we can infer q_4 -> q via biconditional elimination. Finally, from q_4 -> q, q -> q_8 we can infer q_4 -> q_8 via transitivity, which contradicts ~(q_4 -> q_8). Therefore, the answer is no.