Consider the following premises. For all x_10, x_10 will cook. For all x, x will play a game. Can we infer the following from them? There is at least one x for which x will cook and x will play a game.
 From the fact that for all x_10, x_10 will cook we can infer that Sarah is cooking. From the fact that Sarah is cooking we can infer that there is at least one x for which x will cook. Finally, from the fact that there is at least one x for which x will cook, and that for all x, x will play a game we can infer that there is at least one x for which x will cook and x will play a game. Therefore, the answer is yes.