Consider the following premises. If it is sunny, then Susan is an astronaut. It is sunny or it is not cloudy. It is cloudy or Susan is not an astronaut. Can we infer the following from them? If is not true that it is sunny if and only if it is cloudy.
 From the fact that it is cloudy or Susan is not an astronaut we can infer that if Susan were an astronaut, then it is cloudy. From the fact that if it is sunny, then Susan is an astronaut, and that if Susan were an astronaut, then it is cloudy we can infer that if it is sunny, then it is cloudy. From the fact that it is sunny or it is not cloudy we can infer that if it is cloudy, then it is sunny. Finally, from the fact that if it is sunny, then it is cloudy, and that if it is cloudy, then it is sunny we can infer that it is sunny if and only if it is cloudy, which contradicts that If is not true that it is sunny if and only if it is cloudy. Therefore, the answer is no.