Consider the following premises. It is cloudy or it is cold. It is overcast. It is not cloudy. Can we infer the following from them? It is overcast or it is snowing.
 From the fact that it is cloudy or it is cold, and that it is not cloudy we can infer that it is cold. From the fact that it is overcast, and that it is cold we can infer that it is overcast and it is cold. From the fact that it is overcast and it is cold we can infer that it is overcast. Finally, from the fact that it is overcast we can infer that it is overcast or it is snowing. Therefore, the answer is yes.