Consider the following premises. Karen is listening to a song if and only if it is cloudy. If Jessica climbs a mountain, then Karen is listening to a song. It is cloudy if and only if Jessica is a poet. If Jessica were a poet, then Jessica is climbing a mountain. Can we infer the following from them? Jessica is a poet if and only if it is cloudy.
 From the fact that if Jessica were a poet, then Jessica is climbing a mountain, and that if Jessica climbs a mountain, then Karen is listening to a song we can infer that if Jessica were a poet, then Karen is listening to a song. From the fact that it is cloudy if and only if Jessica is a poet we can infer that if it is cloudy, then Jessica is a poet. From the fact that Karen is listening to a song if and only if it is cloudy we can infer that if Karen listens to a song, then it is cloudy. From the fact that if Jessica were a poet, then Karen is listening to a song, and that if Karen listens to a song, then it is cloudy we can infer that if Jessica were a poet, then it is cloudy. Finally, from the fact that if Jessica were a poet, then it is cloudy, and that if it is cloudy, then Jessica is a poet we can infer that Jessica is a poet if and only if it is cloudy. Therefore, the answer is yes.