Consider the following premises. It is cloudy if and only if it is cold. It is cold or Michael is a carpenter. If Michael were a carpenter, then it is cloudy. Can we infer the following from them? It is not cloudy.
 From the fact that it is cloudy if and only if it is cold we can infer that if it is cold, then it is cloudy. Finally, from the fact that if it is cold, then it is cloudy, that if Michael were a carpenter, then it is cloudy, and that it is cold or Michael is a carpenter we can infer that it is cloudy, which contradicts that It is not cloudy. Therefore, the answer is no.