Consider the following premises. Charles is a politician or Michael is working. Charles is not a politician. Barbara is not writing a letter. John is running if and only if Barbara is writing a letter. Can we infer the following from them? John is not running and Michael is working.
 From the fact that John is running if and only if Barbara is writing a letter, and that Barbara is not writing a letter we can infer that John is not running. From the fact that Charles is a politician or Michael is working, and that Charles is not a politician we can infer that Michael is working. Finally, from the fact that John is not running, and that Michael is working we can infer that John is not running and Michael is working. Therefore, the answer is yes.