Consider the following premises. James is cooking if and only if Barbara is a taxi driver. William is poor or it is not late. If it is not late, then James is cooking. William is not poor. Can we infer the following from them? If we can, name the inference rule being used: Barbara is a taxi driver.
 From the fact that James is cooking if and only if Barbara is a taxi driver we can infer that if James cooks, then Barbara is a taxi driver via biconditional elimination. From the fact that William is poor or it is not late we can infer that if it is late, then William is poor via rewriting. From the fact that if it is late, then William is poor, and that William is not poor we can infer that it is not late via modus tollens. From the fact that if it is not late, then James is cooking, and that if James cooks, then Barbara is a taxi driver we can infer that if it is not late, then Barbara is a taxi driver via transitivity. Finally, from the fact that if it is not late, then Barbara is a taxi driver, and that it is not late we can infer that Barbara is a taxi driver via modus ponens. Therefore, the answer is yes.