Consider the following premises. For all z, z will write a letter or z is not an office clerk. For all z, z will not write a letter. There is at least one z for which if z writes a letter, then z is an office clerk. Can we infer the following from them? There is at least one z for which z is not an office clerk.
 From the fact that for all z, z will write a letter or z is not an office clerk we can infer that for all z, if z were an office clerk, then z is writing a letter. From the fact that for all z, if z were an office clerk, then z is writing a letter, and that there is at least one z for which if z writes a letter, then z is an office clerk we can infer that there is at least one z for which z is an office clerk if and only if z will write a letter. Finally, from the fact that there is at least one z for which z is an office clerk if and only if z will write a letter, and that for all z, z will not write a letter we can infer that there is at least one z for which z is not an office clerk. Therefore, the answer is yes.