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