Consider the following premises. It is late or it is not cloudy. It is cloudy or David is not poor. Can we infer the following from them? The fact that David were poor does not imply that it is late.
 From the fact that it is late or it is not cloudy we can infer that if it is cloudy, then it is late. From the fact that it is cloudy or David is not poor we can infer that if David were poor, then it is cloudy. Finally, from the fact that if David were poor, then it is cloudy, and that if it is cloudy, then it is late we can infer that if David were poor, then it is late, which contradicts that The fact that David were poor does not imply that it is late. Therefore, the answer is no.