Consider the following premises. For all y_3, y_3 is a janitor or y_3 will play squash. For all y_3, y_3 is not a nurse. For all y_3, y_3 is a janitor if and only if y_3 will write a letter. For all y_3, y_3 will write a letter if and only if y_3 is a nurse. Can we infer the following from them? There is at least one y_3 for which y_3 will not play squash.
 From the fact that for all y_3, y_3 will write a letter if and only if y_3 is a nurse, and that for all y_3, y_3 is not a nurse we can infer that for all y_3, y_3 will not write a letter. From the fact that for all y_3, y_3 is a janitor if and only if y_3 will write a letter we can infer that for all y_3, if y_3 were a janitor, then y_3 is writing a letter. From the fact that for all y_3, if y_3 were a janitor, then y_3 is writing a letter, and that for all y_3, y_3 will not write a letter we can infer that for all y_3, y_3 is not a janitor. Finally, from the fact that for all y_3, y_3 is a janitor or y_3 will play squash, and that for all y_3, y_3 is not a janitor we can infer that for all y_3, y_3 will play squash, which contradicts that There is at least one y_3 for which y_3 will not play squash. Therefore, the answer is no.