Consider the following premises. For all z, if z were a carpenter, then z is reading a book. Charles is not reading a book. For all z, if z reads a book, then z is a carpenter. Can we infer the following from them? If we can, name the inference rule being used: Charles is a carpenter.
 From the fact that for all z, if z were a carpenter, then z is reading a book, and that for all z, if z reads a book, then z is a carpenter we can infer that for all z, z is a carpenter if and only if z will read a book via universal biconditional introduction. From the fact that for all z, z is a carpenter if and only if z will read a book we can infer that for all z, if z were a carpenter, then z is reading a book via universal biconditional elimination. From the fact that for all z, if z were a carpenter, then z is reading a book we can infer that if Charles were a carpenter, then Charles is reading a book via universal instantiation. Finally, from the fact that if Charles were a carpenter, then Charles is reading a book, and that Charles is not reading a book we can infer that Charles is not a carpenter via modus tollens, which contradicts that Charles is a carpenter. Therefore, the answer is no.