Consider the following premises. For all x_8, x_8 will write a letter. For all x_8, if x_8 writes a letter, then x_8 is driving a car. For all x_8, if x_8 were a janitor, then x_8 is cooking. For all x_8, x_8 is a janitor or x_8 is excited. For all x_8, if x_8 were excited, then x_8 is cooking. Can we infer the following from them? If we can, name the inference rule being used: For all x_8, x_8 will drive a car and x_8 will cook.
 From the fact that for all x_8, if x_8 were a janitor, then x_8 is cooking, that for all x_8, if x_8 were excited, then x_8 is cooking, and that for all x_8, x_8 is a janitor or x_8 is excited we can infer that for all x_8, x_8 will cook via universal disjunction elimination. From the fact that for all x_8, if x_8 writes a letter, then x_8 is driving a car, and that for all x_8, x_8 will write a letter we can infer that for all x_8, x_8 will drive a car via universal modus ponens. Finally, from the fact that for all x_8, x_8 will drive a car, and that for all x_8, x_8 will cook we can infer that for all x_8, x_8 will drive a car and x_8 will cook via universal conjunction. Therefore, the answer is yes.