Consider the following premises. r -> q. q -> p_8. p_8 -> r. p_8 -> q. Can we infer q <-> p_8 from them? If possible, name the inference rules being used at each step.
 From p_8 -> r, r -> q we can infer p_8 -> q via transitivity. Finally, from q -> p_8, p_8 -> q we can infer q <-> p_8 via biconditional introduction. Therefore, the answer is yes.