Consider the following premises. There is at least one y_1 for which y_1 will not cook. For all y_1, if y_1 were a police officer, then y_1 is cooking. For all y_1, if y_1 plays squash, then y_1 is a police officer. For all y_1, if y_1 cooks, then y_1 is playing squash. Can we infer the following from them? For all y_1, y_1 will play squash.
 From the fact that for all y_1, if y_1 plays squash, then y_1 is a police officer, and that for all y_1, if y_1 were a police officer, then y_1 is cooking we can infer that for all y_1, if y_1 plays squash, then y_1 is cooking. From the fact that for all y_1, if y_1 cooks, then y_1 is playing squash, and that for all y_1, if y_1 plays squash, then y_1 is cooking we can infer that for all y_1, y_1 will cook if and only if y_1 will play squash. Finally, from the fact that for all y_1, y_1 will cook if and only if y_1 will play squash, and that there is at least one y_1 for which y_1 will not cook we can infer that there is at least one y_1 for which y_1 will not play squash, which contradicts that For all y_1, y_1 will play squash. Therefore, the answer is no.