Consider the following premises. For all x_14, x_14 will take a plane and x_14 will play squash. There is at least one x_14 for which x_14 will play a game. For all x_14, x_14 will cook. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_14 for which x_14 will cook and x_14 will take a plane.
 From the fact that for all x_14, x_14 will take a plane and x_14 will play squash we can infer that for all x_14, x_14 will take a plane via universal simplification. From the fact that for all x_14, x_14 will take a plane, and that there is at least one x_14 for which x_14 will play a game we can infer that there is at least one x_14 for which x_14 will take a plane and x_14 will play a game via existential conjunction. From the fact that there is at least one x_14 for which x_14 will take a plane and x_14 will play a game we can infer that there is at least one x_14 for which x_14 will take a plane via existential simplification. Finally, from the fact that for all x_14, x_14 will cook, and that there is at least one x_14 for which x_14 will take a plane we can infer that there is at least one x_14 for which x_14 will cook and x_14 will take a plane via existential conjunction. Therefore, the answer is yes.