Consider the following premises. It is not overcast or Charles is cooking. David is not a janitor. Richard is playing squash. It is overcast or David is a janitor. Can we infer the following from them? Charles is cooking and Richard is playing squash.
 From the fact that it is overcast or David is a janitor, and that it is not overcast or Charles is cooking we can infer that David is a janitor or Charles is cooking. From the fact that David is a janitor or Charles is cooking, and that David is not a janitor we can infer that Charles is cooking. Finally, from the fact that Charles is cooking, and that Richard is playing squash we can infer that Charles is cooking and Richard is playing squash. Therefore, the answer is yes.