Consider the following premises. Linda is playing a game if and only if Linda is taking a plane. Linda is not playing a game. Linda is taking a plane if and only if Charles is listening to a song. If Charles listens to a song, then Charles is bored. If Charles were bored, then Charles is listening to a song. Can we infer the following from them? Charles is not bored.
 From the fact that if Charles listens to a song, then Charles is bored, and that if Charles were bored, then Charles is listening to a song we can infer that Charles is listening to a song if and only if Charles is bored. From the fact that Linda is playing a game if and only if Linda is taking a plane, and that Linda is not playing a game we can infer that Linda is not taking a plane. From the fact that Linda is taking a plane if and only if Charles is listening to a song, and that Linda is not taking a plane we can infer that Charles is not listening to a song. From the fact that Charles is listening to a song if and only if Charles is bored we can infer that if Charles were bored, then Charles is listening to a song. Finally, from the fact that if Charles were bored, then Charles is listening to a song, and that Charles is not listening to a song we can infer that Charles is not bored. Therefore, the answer is yes.