Consider the following premises. For all y_3, if y_3 drinks water, then y_3 is a nurse. For all y_3, y_3 will not drink water. There is at least one y_3 for which y_3 will drink water 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 is not a nurse.
 From the fact that there is at least one y_3 for which y_3 will drink water if and only if y_3 is a nurse we can infer that there is at least one y_3 for which if y_3 were a nurse, then y_3 is drinking water. From the fact that for all y_3, if y_3 drinks water, then y_3 is a nurse, and that there is at least one y_3 for which if y_3 were a nurse, then y_3 is drinking water we can infer that there is at least one y_3 for which y_3 will drink water if and only if y_3 is a nurse. Finally, from the fact that there is at least one y_3 for which y_3 will drink water if and only if y_3 is a nurse, and that for all y_3, y_3 will not drink water we can infer that there is at least one y_3 for which y_3 is not a nurse. Therefore, the answer is yes.