Consider the following premises. Jessica is cooking if and only if James is taking a plane. If Elisabeth were a writer, then Jessica is cooking. If James takes a plane, then Elisabeth is a writer. Can we infer the following from them? If we can, name the inference rule being used: Jessica is cooking if and only if Elisabeth is a writer.
 From the fact that Jessica is cooking if and only if James is taking a plane we can infer that if Jessica cooks, then James is taking a plane via biconditional elimination. From the fact that if Jessica cooks, then James is taking a plane, and that if James takes a plane, then Elisabeth is a writer we can infer that if Jessica cooks, then Elisabeth is a writer via transitivity. Finally, from the fact that if Jessica cooks, then Elisabeth is a writer, and that if Elisabeth were a writer, then Jessica is cooking we can infer that Jessica is cooking if and only if Elisabeth is a writer via biconditional introduction. Therefore, the answer is yes.