Consider the following premises. It is raining if and only if Mary is listening to a song. If Linda were a musician, then it is cold. If Mary listens to a song, then Linda is a musician. Can we infer the following from them? If we can, name the inference rule being used: The fact that it rains does not imply that it is cold.
 From the fact that it is raining if and only if Mary is listening to a song we can infer that if it rains, then Mary is listening to a song via biconditional elimination. From the fact that if Mary listens to a song, then Linda is a musician, and that if Linda were a musician, then it is cold we can infer that if Mary listens to a song, then it is cold via transitivity. Finally, from the fact that if it rains, then Mary is listening to a song, and that if Mary listens to a song, then it is cold we can infer that if it rains, then it is cold via transitivity, which contradicts that The fact that it rains does not imply that it is cold. Therefore, the answer is no.