Consider the following premises. Robert is climbing a mountain if and only if it is windy. Robert is climbing a mountain or it is not cloudy. If it is windy, then it is cloudy. Can we infer the following from them? Robert is climbing a mountain if and only if it is cloudy.
 From the fact that Robert is climbing a mountain or it is not cloudy we can infer that if it is cloudy, then Robert is climbing a mountain. From the fact that Robert is climbing a mountain if and only if it is windy we can infer that if Robert climbs a mountain, then it is windy. From the fact that if Robert climbs a mountain, then it is windy, and that if it is windy, then it is cloudy we can infer that if Robert climbs a mountain, then it is cloudy. Finally, from the fact that if Robert climbs a mountain, then it is cloudy, and that if it is cloudy, then Robert is climbing a mountain we can infer that Robert is climbing a mountain if and only if it is cloudy. Therefore, the answer is yes.