Consider the following premises. There is at least one z for which if z were a police officer, then z is reading a book. For all z, if z were a police officer, then z is reading a book. For all z, if z reads a book, then z is a police officer. Can we infer the following from them? For all z, if is not true that z will read a book if and only if z is a police officer.
 From the fact that for all z, if z reads a book, then z is a police officer, and that there is at least one z for which if z were a police officer, then z is reading a book we can infer that there is at least one z for which z will read a book if and only if z is a police officer. From the fact that there is at least one z for which z will read a book if and only if z is a police officer we can infer that there is at least one z for which if z reads a book, then z is a police officer. Finally, from the fact that there is at least one z for which if z reads a book, then z is a police officer, and that for all z, if z were a police officer, then z is reading a book we can infer that there is at least one z for which z will read a book if and only if z is a police officer, which contradicts that For all z, if is not true that z will read a book if and only if z is a police officer. Therefore, the answer is no.