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