Consider the following premises. Patricia is poor or Susan is a politician. It is overcast or Susan is not a politician. If William were a carpenter, then it is not overcast. If Patricia were poor, then it is overcast. Can we infer the following from them? William is a carpenter.
 From the fact that it is overcast or Susan is not a politician we can infer that if Susan were a politician, then it is overcast. From the fact that if Patricia were poor, then it is overcast, that if Susan were a politician, then it is overcast, and that Patricia is poor or Susan is a politician we can infer that it is overcast. Finally, from the fact that if William were a carpenter, then it is not overcast, and that it is overcast we can infer that William is not a carpenter, which contradicts that William is a carpenter. Therefore, the answer is no.