Consider the following premises. Barbara is a sailor if and only if Karen is listening to a song. If David plays a game, then Barbara is a sailor. Karen is not listening to a song. Can we infer the following from them? If we can, name the inference rule being used: David is not playing a game.
 From the fact that Barbara is a sailor if and only if Karen is listening to a song, and that Karen is not listening to a song we can infer that Barbara is not a sailor via biconditional elimination. Finally, from the fact that if David plays a game, then Barbara is a sailor, and that Barbara is not a sailor we can infer that David is not playing a game via modus tollens. Therefore, the answer is yes.