Consider the following premises. p -> r_1. r_1 -> p. p <-> u. Can we infer r_1 -> u from them?
 From p -> r_1, r_1 -> p we can infer p <-> r_1. From p <-> r_1 we can infer r_1 -> p. From p <-> u we can infer p -> u. Finally, from r_1 -> p, p -> u we can infer r_1 -> u. Therefore, the answer is yes.