Consider the following premises. For all x_10, x_10 will work or x_10 is a police officer. For all x_10, x_10 will climb a mountain. For all x_10, x_10 will not work or x_10 will cook. For all x_10, if x_10 were a police officer, then x_10 is not climbing a mountain. Can we infer the following from them? If we can, name the inference rule being used: For all x_10, x_10 will cook or x_10 is poor.
 From the fact that for all x_10, x_10 will work or x_10 is a police officer, and that for all x_10, x_10 will not work or x_10 will cook we can infer that for all x_10, x_10 is a police officer or x_10 will cook via universal resolution. From the fact that for all x_10, if x_10 were a police officer, then x_10 is not climbing a mountain, and that for all x_10, x_10 will climb a mountain we can infer that for all x_10, x_10 is not a police officer via universal modus tollens. From the fact that for all x_10, x_10 is a police officer or x_10 will cook, and that for all x_10, x_10 is not a police officer we can infer that for all x_10, x_10 will cook via universal disjunctive syllogism. Finally, from the fact that for all x_10, x_10 will cook we can infer that for all x_10, x_10 will cook or x_10 is poor via universal addition. Therefore, the answer is yes.