Consider the following premises. James is reading a book if and only if Charles is sad. Patricia is an office clerk if and only if James is reading a book. Patricia is not an office clerk. Can we infer the following from them? If we can, name the inference rule being used: Charles is not sad.
 From the fact that James is reading a book if and only if Charles is sad we can infer that if Charles were sad, then James is reading a book via biconditional elimination. From the fact that Patricia is an office clerk if and only if James is reading a book, and that Patricia is not an office clerk we can infer that James is not reading a book via biconditional elimination. Finally, from the fact that if Charles were sad, then James is reading a book, and that James is not reading a book we can infer that Charles is not sad via modus tollens. Therefore, the answer is yes.