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