Consider the following premises. David is listening to a song if and only if Robert is playing a game. If Robert plays a game, then William is an artist. William is an artist if and only if it is late. It is not late. Can we infer the following from them? If we can, name the inference rule being used: David is listening to a song.
 From the fact that William is an artist if and only if it is late, and that it is not late we can infer that William is not an artist via biconditional elimination. From the fact that if Robert plays a game, then William is an artist, and that William is not an artist we can infer that Robert is not playing a game via modus tollens. Finally, from the fact that David is listening to a song if and only if Robert is playing a game, and that Robert is not playing a game we can infer that David is not listening to a song via biconditional elimination, which contradicts that David is listening to a song. Therefore, the answer is no.