Consider the following premises. If Patricia were happy, then it is cloudy. Patricia is happy or Sarah is a nurse. It is cloudy or Sarah is not a nurse. If William were a lawyer, then it is not cloudy. Can we infer the following from them? William is not a lawyer.
 From the fact that it is cloudy or Sarah is not a nurse we can infer that if Sarah were a nurse, then it is cloudy. From the fact that if Patricia were happy, then it is cloudy, that if Sarah were a nurse, then it is cloudy, and that Patricia is happy or Sarah is a nurse we can infer that it is cloudy. Finally, from the fact that if William were a lawyer, then it is not cloudy, and that it is cloudy we can infer that William is not a lawyer. Therefore, the answer is yes.