Consider the following premises. For all x_1, x_1 will play a game or x_1 will play squash. There is at least one x_1 for which x_1 will cook or x_1 will not play squash. For all x_1, x_1 will not play a game. Can we infer the following from them? There is at least one x_1 for which x_1 will cook.
 From the fact that there is at least one x_1 for which x_1 will cook or x_1 will not play squash we can infer that there is at least one x_1 for which if x_1 plays squash, then x_1 is cooking. From the fact that for all x_1, x_1 will play a game or x_1 will play squash, and that for all x_1, x_1 will not play a game we can infer that for all x_1, x_1 will play squash. Finally, from the fact that there is at least one x_1 for which if x_1 plays squash, then x_1 is cooking, and that for all x_1, x_1 will play squash we can infer that there is at least one x_1 for which x_1 will cook. Therefore, the answer is yes.