Consider the following premises. r_2 -> w. r_2 or ~u. w -> u. Can we infer u <-> w from them?
 From r_2 or ~u we can infer u -> r_2. From u -> r_2, r_2 -> w we can infer u -> w. Finally, from u -> w, w -> u we can infer u <-> w. Therefore, the answer is yes.