Consider the following premises. Susan is playing tennis or David is reading a book. Susan is playing tennis if and only if Jessica is a janitor. Jessica is not a janitor. Can we infer the following from them? David is reading a book or Joseph is a bartender.
 From the fact that Susan is playing tennis if and only if Jessica is a janitor, and that Jessica is not a janitor we can infer that Susan is not playing tennis. From the fact that Susan is playing tennis or David is reading a book, and that Susan is not playing tennis we can infer that David is reading a book. Finally, from the fact that David is reading a book we can infer that David is reading a book or Joseph is a bartender. Therefore, the answer is yes.