Consider the following premises. Karen is climbing a mountain. For all x_10, if x_10 drinks water, then x_10 is a carpenter. For all x_10, x_10 will drink water. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_10 for which x_10 will climb a mountain and x_10 is a carpenter.
 From the fact that for all x_10, if x_10 drinks water, then x_10 is a carpenter, and that for all x_10, x_10 will drink water we can infer that for all x_10, x_10 is a carpenter via universal modus ponens. From the fact that Karen is climbing a mountain we can infer that there is at least one x_10 for which x_10 will climb a mountain via existential generalization. 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 is a carpenter we can infer that there is at least one x_10 for which x_10 will climb a mountain and x_10 is a carpenter via existential conjunction. Therefore, the answer is yes.