Consider the following premises. It is not cold. Jessica is a janitor. It is cold if and only if Jessica is a janitor. Can we infer the following from them? John is writing a letter.
 From the fact that it is cold if and only if Jessica is a janitor, and that it is not cold we can infer that Jessica is not a janitor. From the fact that Jessica is not a janitor we can infer that Jessica is not a janitor or John is writing a letter. Finally, from the fact that Jessica is not a janitor or John is writing a letter, and that Jessica is a janitor we can infer that John is writing a letter. Therefore, the answer is yes. Notice, however, that the premises were contradictory, so we can infer anything from them.