Consider the following premises. It is not snowing. It is snowing or Michael is not playing tennis. If it is overcast, then Michael is playing tennis. Can we infer the following from them? It is not overcast.
 From the fact that it is snowing or Michael is not playing tennis we can infer that if Michael plays tennis, then it is snowing. From the fact that if it is overcast, then Michael is playing tennis, and that if Michael plays tennis, then it is snowing we can infer that if it is overcast, then it is snowing. Finally, from the fact that if it is overcast, then it is snowing, and that it is not snowing we can infer that it is not overcast. Therefore, the answer is yes.