Consider the following premises. For all x_6, x_6 will write a letter if and only if x_6 is a nurse. For all x_6, if x_6 were a nurse, then x_6 is not cooking. For all x_6, x_6 will cook. For all x_6, x_6 will drink water if and only if x_6 will write a letter. Can we infer the following from them? For all x_6, x_6 will not drink water.
 From the fact that for all x_6, if x_6 were a nurse, then x_6 is not cooking, and that for all x_6, x_6 will cook we can infer that for all x_6, x_6 is not a nurse. From the fact that for all x_6, x_6 will write a letter if and only if x_6 is a nurse, and that for all x_6, x_6 is not a nurse we can infer that for all x_6, x_6 will not write a letter. Finally, from the fact that for all x_6, x_6 will drink water if and only if x_6 will write a letter, and that for all x_6, x_6 will not write a letter we can infer that for all x_6, x_6 will not drink water. Therefore, the answer is yes.