Consider the following premises. Mary is a nurse if and only if Thomas is an astronaut. If it rains, then Jessica is happy. Mary is not a nurse. Jessica is happy if and only if Thomas is an astronaut. Can we infer the following from them? It is not raining.
 From the fact that Mary is a nurse if and only if Thomas is an astronaut, and that Mary is not a nurse we can infer that Thomas is not an astronaut. From the fact that Jessica is happy if and only if Thomas is an astronaut, and that Thomas is not an astronaut we can infer that Jessica is not happy. Finally, from the fact that if it rains, then Jessica is happy, and that Jessica is not happy we can infer that it is not raining. Therefore, the answer is yes.