Consider the following premises. If Jessica writes a letter, then David is running. If Karen listens to a song, then Barbara is an artist. If David goes running, then it is sunny. If it is sunny, then Karen is listening to a song. If Barbara were an artist, then Jessica is writing a letter. Can we infer the following from them? David is running if and only if Jessica is writing a letter.
 From the fact that if David goes running, then it is sunny, and that if it is sunny, then Karen is listening to a song we can infer that if David goes running, then Karen is listening to a song. From the fact that if David goes running, then Karen is listening to a song, and that if Karen listens to a song, then Barbara is an artist we can infer that if David goes running, then Barbara is an artist. From the fact that if David goes running, then Barbara is an artist, and that if Barbara were an artist, then Jessica is writing a letter we can infer that if David goes running, then Jessica is writing a letter. Finally, from the fact that if David goes running, then Jessica is writing a letter, and that if Jessica writes a letter, then David is running we can infer that David is running if and only if Jessica is writing a letter. Therefore, the answer is yes.