Consider the following premises. For all x_10, x_10 is a police officer. For all x_10, if x_10 were a police officer, then x_10 is cooking. There is at least one x_10 for which x_10 will climb a mountain and x_10 will drink water. Can we infer the following from them? For all x_10, either x_10 will climb a mountain or x_10 will cook are not true.
 From the fact that there is at least one x_10 for which x_10 will climb a mountain and x_10 will drink water we can infer that there is at least one x_10 for which x_10 will climb a mountain. From the fact that for all x_10, if x_10 were a police officer, then x_10 is cooking, and that for all x_10, x_10 is a police officer we can infer that for all x_10, x_10 will cook. Finally, from the fact that there is at least one x_10 for which x_10 will climb a mountain, and that for all x_10, x_10 will cook we can infer that there is at least one x_10 for which x_10 will climb a mountain and x_10 will cook, which contradicts that For all x_10, either x_10 will climb a mountain or x_10 will cook are not true. Therefore, the answer is no.