Consider the following premises. Joseph is not a nurse. If Richard takes a plane, then Patricia is excited. If Patricia were excited, then Richard is taking a plane. Richard is taking a plane if and only if Joseph is a nurse. Can we infer the following from them? If we can, name the inference rule being used: Patricia is not excited.
 From the fact that Richard is taking a plane if and only if Joseph is a nurse, and that Joseph is not a nurse we can infer that Richard is not taking a plane via biconditional elimination. From the fact that if Richard takes a plane, then Patricia is excited, and that if Patricia were excited, then Richard is taking a plane we can infer that Richard is taking a plane if and only if Patricia is excited via biconditional introduction. From the fact that Richard is taking a plane if and only if Patricia is excited we can infer that if Patricia were excited, then Richard is taking a plane via biconditional elimination. Finally, from the fact that if Patricia were excited, then Richard is taking a plane, and that Richard is not taking a plane we can infer that Patricia is not excited via modus tollens. Therefore, the answer is yes.