Consider the following premises. Barbara is excited if and only if Robert is reading a book. For all x, if x were excited, then x is rich. For all x, x is not rich. Can we infer the following from them? If we can, name the inference rule being used: Robert is not reading a book.
 From the fact that for all x, if x were excited, then x is rich, and that for all x, x is not rich we can infer that for all x, x is not excited via universal modus tollens. From the fact that for all x, x is not excited we can infer that Barbara is not excited via universal instantiation. Finally, from the fact that Barbara is excited if and only if Robert is reading a book, and that Barbara is not excited we can infer that Robert is not reading a book via biconditional elimination. Therefore, the answer is yes.