Consider the following premises. ~r_2. r_2 -> u. r_2 <-> u. w. Can we infer ~u and w from them? If possible, name the inference rules being used at each step.
 From r_2 <-> u we can infer u -> r_2 via biconditional elimination. From r_2 -> u, u -> r_2 we can infer r_2 <-> u via biconditional introduction. From r_2 <-> u, ~r_2 we can infer ~u via biconditional elimination. Finally, from ~u, w we can infer ~u and w via conjunction. Therefore, the answer is yes.