Consider the following premises. For all z, z is not a writer or z is a mechanic. For all z, z is a writer. There is at least one z for which z will not write a letter. Can we infer the following from them? There is at least one z for which z is a mechanic.
 From the fact that for all z, z is a writer we can infer that for all z, z is a writer or z will write a letter. From the fact that for all z, z is a writer or z will write a letter, and that for all z, z is not a writer or z is a mechanic we can infer that for all z, z will write a letter or z is a mechanic. Finally, from the fact that for all z, z will write a letter or z is a mechanic, and that there is at least one z for which z will not write a letter we can infer that there is at least one z for which z is a mechanic. Therefore, the answer is yes.