Consider the following premises. It is cloudy or Jennifer is not a poet. Jennifer is a poet or it is not cloudy. Can we infer the following from them? If is not true that Jennifer is a poet if and only if it is cloudy.
 From the fact that it is cloudy or Jennifer is not a poet we can infer that if Jennifer were a poet, then it is cloudy. From the fact that Jennifer is a poet or it is not cloudy we can infer that if it is cloudy, then Jennifer is a poet. Finally, from the fact that if Jennifer were a poet, then it is cloudy, and that if it is cloudy, then Jennifer is a poet we can infer that Jennifer is a poet if and only if it is cloudy, which contradicts that If is not true that Jennifer is a poet if and only if it is cloudy. Therefore, the answer is no.