Consider the following premises. For all x_2, x_2 will cook or x_2 will write a letter. For all x_2, x_2 will not write a letter. For all x_2, x_2 will not cook or x_2 is a nurse. Can we infer the following from them? If we can, name the inference rule being used: For all x_2, x_2 is a nurse.
 From the fact that for all x_2, x_2 will cook or x_2 will write a letter, and that for all x_2, x_2 will not cook or x_2 is a nurse we can infer that for all x_2, x_2 will write a letter or x_2 is a nurse via universal resolution. Finally, from the fact that for all x_2, x_2 will write a letter or x_2 is a nurse, and that for all x_2, x_2 will not write a letter we can infer that for all x_2, x_2 is a nurse via universal disjunctive syllogism. Therefore, the answer is yes.