Consider the following premises. r_3 <-> w_1. w_1 -> ~u. u. Can we infer r_3 from them? If possible, name the inference rules being used at each step.
 From r_3 <-> w_1 we can infer r_3 -> w_1 via biconditional elimination. From w_1 -> ~u, u we can infer ~w_1 via modus tollens. Finally, from r_3 -> w_1, ~w_1 we can infer ~r_3 via modus tollens, which contradicts r_3. Therefore, the answer is no.