Consider the following premises. For all x_2, x_2 is not a police officer. There is at least one x_2 for which x_2 is a nurse. For all x_2, x_2 is a police officer or x_2 will write a letter. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_2 for which x_2 will write a letter and x_2 is a nurse.
 From the fact that for all x_2, x_2 is a police officer or x_2 will write a letter, and that for all x_2, x_2 is not a police officer we can infer that for all x_2, x_2 will write a letter via universal disjunctive syllogism. Finally, from the fact that for all x_2, x_2 will write a letter, and that there is at least one x_2 for which x_2 is a nurse we can infer that there is at least one x_2 for which x_2 will write a letter and x_2 is a nurse via existential conjunction. Therefore, the answer is yes.