Consider the following premises. It is snowing if and only if James is climbing a mountain. If it is cold, then it is snowing. It is overcast if and only if it is cold. James is not climbing a mountain. Can we infer the following from them? It is not overcast.
 From the fact that it is snowing if and only if James is climbing a mountain, and that James is not climbing a mountain we can infer that it is not snowing. From the fact that if it is cold, then it is snowing, and that it is not snowing we can infer that it is not cold. From the fact that it is overcast if and only if it is cold we can infer that if it is overcast, then it is cold. Finally, from the fact that if it is overcast, then it is cold, and that it is not cold we can infer that it is not overcast. Therefore, the answer is yes.