Consider the following premises. Charles is not a janitor or it is late. Charles is a janitor or it is raining. William is a lawyer if and only if it is late. It is not raining. Can we infer the following from them? William is a lawyer.
 From the fact that Charles is a janitor or it is raining, and that Charles is not a janitor or it is late we can infer that it is raining or it is late. From the fact that William is a lawyer if and only if it is late we can infer that if it is late, then William is a lawyer. From the fact that it is raining or it is late, and that it is not raining we can infer that it is late. Finally, from the fact that if it is late, then William is a lawyer, and that it is late we can infer that William is a lawyer. Therefore, the answer is yes.