Consider the following premises. If Susan doesn't cook, then Barbara is a writer. It is not late. It is late if and only if Susan is cooking. Can we infer the following from them? If we can, name the inference rule being used: Barbara is a writer.
 From the fact that it is late if and only if Susan is cooking, and that it is not late we can infer that Susan is not cooking via biconditional elimination. Finally, from the fact that if Susan doesn't cook, then Barbara is a writer, and that Susan is not cooking we can infer that Barbara is a writer via modus ponens. Therefore, the answer is yes.