Consider the following premises. For all z, z will not play a game. For all z, z is a musician if and only if z will read a book. For all z, z will read a book if and only if z will play a game. Can we infer the following from them? If we can, name the inference rule being used: For all z, z is not a musician.
 From the fact that for all z, z is a musician if and only if z will read a book we can infer that for all z, if z were a musician, then z is reading a book via universal biconditional elimination. From the fact that for all z, z will read a book if and only if z will play a game, and that for all z, z will not play a game we can infer that for all z, z will not read a book via universal biconditional elimination. Finally, from the fact that for all z, if z were a musician, then z is reading a book, and that for all z, z will not read a book we can infer that for all z, z is not a musician via universal modus tollens. Therefore, the answer is yes.