Consider the following premises. If Elisabeth listens to a song, then Linda is curious. If Patricia works, then Elisabeth is listening to a song. If Michael plays a game, then Patricia is working. If Linda were curious, then Michael is playing a game. Can we infer the following from them? If we can, name the inference rule being used: The fact that Elisabeth listens to a song does not imply that Michael is playing a game.
 From the fact that if Michael plays a game, then Patricia is working, and that if Patricia works, then Elisabeth is listening to a song we can infer that if Michael plays a game, then Elisabeth is listening to a song via transitivity. Finally, from the fact that if Elisabeth listens to a song, then Linda is curious, and that if Linda were curious, then Michael is playing a game we can infer that if Elisabeth listens to a song, then Michael is playing a game via transitivity, which contradicts that The fact that Elisabeth listens to a song does not imply that Michael is playing a game. Therefore, the answer is no.