Consider the following premises. It is late and Jennifer is a lawyer. Patricia is not listening to a song. If it rains, then Patricia is listening to a song. If Patricia listens to a song, then it is raining. Can we infer the following from them? If we can, name the inference rule being used: It is raining.
 From the fact that if Patricia listens to a song, then it is raining, and that if it rains, then Patricia is listening to a song we can infer that Patricia is listening to a song if and only if it is raining via biconditional introduction. From the fact that it is late and Jennifer is a lawyer we can infer that it is late via simplification. Finally, from the fact that Patricia is listening to a song if and only if it is raining, and that Patricia is not listening to a song we can infer that it is not raining via biconditional elimination, which contradicts that It is raining. Therefore, the answer is no.