Consider the following premises. r_2 -> r_4. r_2 and u. Can we infer r_4 from them? If possible, name the inference rules being used at each step.
 From r_2 and u we can infer r_2 via simplification. Finally, from r_2 -> r_4, r_2 we can infer r_4 via modus ponens. Therefore, the answer is yes.