Consider the following premises. For all x_9, if x_9 were a nurse, then x_9 is writing a letter. For all x_9, if x_9 were a janitor, then x_9 is a nurse. There is at least one x_9 for which x_9 will write a letter if and only if x_9 is a janitor. Can we infer the following from them? For all x_9, if is not true that x_9 will write a letter if and only if x_9 is a nurse.
 From the fact that there is at least one x_9 for which x_9 will write a letter if and only if x_9 is a janitor we can infer that there is at least one x_9 for which if x_9 writes a letter, then x_9 is a janitor. From the fact that there is at least one x_9 for which if x_9 writes a letter, then x_9 is a janitor, and that for all x_9, if x_9 were a janitor, then x_9 is a nurse we can infer that there is at least one x_9 for which if x_9 writes a letter, then x_9 is a nurse. Finally, from the fact that there is at least one x_9 for which if x_9 writes a letter, then x_9 is a nurse, and that for all x_9, if x_9 were a nurse, then x_9 is writing a letter we can infer that there is at least one x_9 for which x_9 will write a letter if and only if x_9 is a nurse, which contradicts that For all x_9, if is not true that x_9 will write a letter if and only if x_9 is a nurse. Therefore, the answer is no.