Consider the following premises. For all x_2, x_2 is poor or x_2 is a scientist. For all x_2, x_2 is not poor or x_2 will cook. There is at least one x_2 for which x_2 is not a scientist. 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 cook.
 From the fact that for all x_2, x_2 is poor or x_2 is a scientist, and that for all x_2, x_2 is not poor or x_2 will cook we can infer that for all x_2, x_2 is a scientist or x_2 will cook via universal resolution. Finally, from the fact that for all x_2, x_2 is a scientist or x_2 will cook, and that there is at least one x_2 for which x_2 is not a scientist we can infer that there is at least one x_2 for which x_2 will cook via existential disjunctive syllogism. Therefore, the answer is yes.