Consider the following premises. It is overcast. Joseph is a poet. Joseph is a poet if and only if Patricia is sad. Can we infer the following from them? It is overcast and Patricia is sad.
 From the fact that Joseph is a poet if and only if Patricia is sad we can infer that if Joseph were a poet, then Patricia is sad. From the fact that if Joseph were a poet, then Patricia is sad, and that Joseph is a poet we can infer that Patricia is sad. Finally, from the fact that it is overcast, and that Patricia is sad we can infer that it is overcast and Patricia is sad. Therefore, the answer is yes.