Consider the following premises. William is curious if and only if Karen is a bartender. William is curious if and only if Barbara is a police officer. If Karen were a bartender, then John is not a carpenter. John is a carpenter. Can we infer the following from them? If we can, name the inference rule being used: Barbara is a police officer.
 From the fact that if Karen were a bartender, then John is not a carpenter, and that John is a carpenter we can infer that Karen is not a bartender via modus tollens. From the fact that William is curious if and only if Barbara is a police officer we can infer that if Barbara were a police officer, then William is curious via biconditional elimination. From the fact that William is curious if and only if Karen is a bartender, and that Karen is not a bartender we can infer that William is not curious via biconditional elimination. Finally, from the fact that if Barbara were a police officer, then William is curious, and that William is not curious we can infer that Barbara is not a police officer via modus tollens, which contradicts that Barbara is a police officer. Therefore, the answer is no.