Consider the following premises. It is sunny or Sarah is a politician. It is overcast if and only if Sarah is a politician. It is overcast or it is not sunny. Can we infer the following from them? It is overcast.
 From the fact that it is overcast if and only if Sarah is a politician we can infer that if Sarah were a politician, then it is overcast. From the fact that it is overcast or it is not sunny we can infer that if it is sunny, then it is overcast. Finally, from the fact that if it is sunny, then it is overcast, that if Sarah were a politician, then it is overcast, and that it is sunny or Sarah is a politician we can infer that it is overcast. Therefore, the answer is yes.