Consider the following premises. Jessica is a nurse if and only if David is playing tennis. If James were excited, then David is playing tennis. Jessica is not a nurse. Can we infer the following from them? If we can, name the inference rule being used: James is excited.
 From the fact that Jessica is a nurse if and only if David is playing tennis we can infer that if David plays tennis, then Jessica is a nurse via biconditional elimination. From the fact that if David plays tennis, then Jessica is a nurse, and that Jessica is not a nurse we can infer that David is not playing tennis via modus tollens. Finally, from the fact that if James were excited, then David is playing tennis, and that David is not playing tennis we can infer that James is not excited via modus tollens, which contradicts that James is excited. Therefore, the answer is no.