Consider the following premises. It is cloudy. John is taking a plane. It is overcast if and only if Barbara is listening to a song. If Barbara listens to a song, then John is not taking a plane. Can we infer the following from them? It is overcast.
 From the fact that if Barbara listens to a song, then John is not taking a plane, and that John is taking a plane we can infer that Barbara is not listening to a song. Finally, from the fact that it is overcast if and only if Barbara is listening to a song, and that Barbara is not listening to a song we can infer that it is not overcast, which contradicts that It is overcast. Therefore, the answer is no.