Consider the following premises. Jessica is a carpenter if and only if it is raining. Jessica is a carpenter if and only if it is raining. Can we infer the following from them? It is raining if and only if Jessica is a carpenter.
 From the fact that Jessica is a carpenter if and only if it is raining we can infer that if it rains, then Jessica is a carpenter. From the fact that Jessica is a carpenter if and only if it is raining we can infer that if Jessica were a carpenter, then it is raining. Finally, from the fact that if it rains, then Jessica is a carpenter, and that if Jessica were a carpenter, then it is raining we can infer that it is raining if and only if Jessica is a carpenter. Therefore, the answer is yes.