Consider the following premises. David is a mechanic. Karen is an artist. If Jessica listens to a song, then David is a mechanic. If David were a mechanic, then Jessica is listening to a song. Can we infer the following from them? Jessica is not listening to a song.
 From the fact that David is a mechanic, and that Karen is an artist we can infer that David is a mechanic and Karen is an artist. From the fact that if Jessica listens to a song, then David is a mechanic, and that if David were a mechanic, then Jessica is listening to a song we can infer that Jessica is listening to a song if and only if David is a mechanic. From the fact that David is a mechanic and Karen is an artist we can infer that David is a mechanic. From the fact that Jessica is listening to a song if and only if David is a mechanic we can infer that if David were a mechanic, then Jessica is listening to a song. Finally, from the fact that if David were a mechanic, then Jessica is listening to a song, and that David is a mechanic we can infer that Jessica is listening to a song, which contradicts that Jessica is not listening to a song. Therefore, the answer is no.