Consider the following premises. If David goes running, then Jennifer is not writing a letter. Jennifer is writing a letter. Charles is sleeping if and only if David is not running. Can we infer the following from them? If we can, name the inference rule being used: Charles is sleeping.
 From the fact that if David goes running, then Jennifer is not writing a letter, and that Jennifer is writing a letter we can infer that David is not running via modus tollens. From the fact that Charles is sleeping if and only if David is not running we can infer that if David doesn't go running, then Charles is sleeping via biconditional elimination. Finally, from the fact that if David doesn't go running, then Charles is sleeping, and that David is not running we can infer that Charles is sleeping via modus ponens. Therefore, the answer is yes.