Consider the following premises. Karen is writing a letter if and only if Barbara is driving a car. Karen is writing a letter if and only if James is playing tennis. James is not playing tennis. If Michael were a bartender, then Barbara is driving a car. Can we infer the following from them? If we can, name the inference rule being used: Michael is a bartender.
 From the fact that Karen is writing a letter if and only if James is playing tennis, and that James is not playing tennis we can infer that Karen is not writing a letter via biconditional elimination. From the fact that Karen is writing a letter if and only if Barbara is driving a car, and that Karen is not writing a letter we can infer that Barbara is not driving a car via biconditional elimination. Finally, from the fact that if Michael were a bartender, then Barbara is driving a car, and that Barbara is not driving a car we can infer that Michael is not a bartender via modus tollens, which contradicts that Michael is a bartender. Therefore, the answer is no.