Consider the following premises. For all x_11, x_11 is a cashier or x_11 will cook. For all x_11, x_11 is not a cashier or x_11 will write a letter. There is at least one x_11 for which x_11 will not cook. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_11 for which x_11 will write a letter or x_11 will drive a car.
 From the fact that for all x_11, x_11 is a cashier or x_11 will cook, and that for all x_11, x_11 is not a cashier or x_11 will write a letter we can infer that for all x_11, x_11 will cook or x_11 will write a letter via universal resolution. From the fact that for all x_11, x_11 will cook or x_11 will write a letter, and that there is at least one x_11 for which x_11 will not cook we can infer that there is at least one x_11 for which x_11 will write a letter via existential disjunctive syllogism. Finally, from the fact that there is at least one x_11 for which x_11 will write a letter we can infer that there is at least one x_11 for which x_11 will write a letter or x_11 will drive a car via existential addition. Therefore, the answer is yes.