Consider the following premises. For all x_5, if x_5 drives a car, then x_5 is writing a letter. For all x_5, x_5 will drive a car. For all x_5, x_5 will cook. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_5 for which x_5 will not write a letter.
 From the fact that for all x_5, x_5 will drive a car, and that for all x_5, x_5 will cook we can infer that for all x_5, x_5 will drive a car and x_5 will cook via universal conjunction. From the fact that for all x_5, x_5 will drive a car and x_5 will cook we can infer that for all x_5, x_5 will drive a car via universal simplification. Finally, from the fact that for all x_5, if x_5 drives a car, then x_5 is writing a letter, and that for all x_5, x_5 will drive a car we can infer that for all x_5, x_5 will write a letter via universal modus ponens, which contradicts that There is at least one x_5 for which x_5 will not write a letter. Therefore, the answer is no.