Consider the following premises. If it rains, then Linda is sad. If Barbara were a musician, then Linda is sad. It is not raining. If Linda were sad, then Barbara is a musician. If Linda were sad, then it is raining. Can we infer the following from them? If we can, name the inference rule being used: Barbara is a musician.
 From the fact that if Linda were sad, then it is raining, and that if it rains, then Linda is sad we can infer that Linda is sad if and only if it is raining via biconditional introduction. From the fact that if Barbara were a musician, then Linda is sad, and that if Linda were sad, then Barbara is a musician we can infer that Barbara is a musician if and only if Linda is sad via biconditional introduction. From the fact that Linda is sad if and only if it is raining, and that it is not raining we can infer that Linda is not sad via biconditional elimination. Finally, from the fact that Barbara is a musician if and only if Linda is sad, and that Linda is not sad we can infer that Barbara is not a musician via biconditional elimination, which contradicts that Barbara is a musician. Therefore, the answer is no.