Consider the following premises. John is a server or Barbara is a janitor. It is cold. John is not a server. If it rains, then Barbara is not a janitor. Can we infer the following from them? It is not raining.
 From the fact that John is a server or Barbara is a janitor, and that John is not a server we can infer that Barbara is a janitor. Finally, from the fact that if it rains, then Barbara is not a janitor, and that Barbara is a janitor we can infer that it is not raining. Therefore, the answer is yes.