Consider the following premises. It is cloudy or it is not raining. Susan is a politician or it is raining. It is cloudy if and only if Susan is a politician. Can we infer the following from them? It is not cloudy.
 From the fact that it is cloudy if and only if Susan is a politician we can infer that if Susan were a politician, then it is cloudy. From the fact that it is cloudy or it is not raining we can infer that if it rains, then it is cloudy. Finally, from the fact that if Susan were a politician, then it is cloudy, that if it rains, then it is cloudy, and that Susan is a politician or it is raining we can infer that it is cloudy, which contradicts that It is not cloudy. Therefore, the answer is no.