Consider the following premises. If William takes a plane, then it is raining. If Sarah were a soldier, then it is late. If it rains, then William is taking a plane. William is taking a plane if and only if Sarah is a soldier. It is not late. Can we infer the following from them? It is not raining.
 From the fact that if it rains, then William is taking a plane, and that if William takes a plane, then it is raining we can infer that it is raining if and only if William is taking a plane. From the fact that if Sarah were a soldier, then it is late, and that it is not late we can infer that Sarah is not a soldier. From the fact that William is taking a plane if and only if Sarah is a soldier, and that Sarah is not a soldier we can infer that William is not taking a plane. Finally, from the fact that it is raining if and only if William is taking a plane, and that William is not taking a plane we can infer that it is not raining. Therefore, the answer is yes.