Consider the following premises. p_8 <-> q. q -> r_1. r_1 -> r. Can we infer p_8 -> r from them? If possible, name the inference rules being used at each step.
 From p_8 <-> q we can infer p_8 -> q via biconditional elimination. From p_8 -> q, q -> r_1 we can infer p_8 -> r_1 via transitivity. Finally, from p_8 -> r_1, r_1 -> r we can infer p_8 -> r via transitivity. Therefore, the answer is yes.