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