Consider the following premises. If Linda were a nurse, then it is late. If it is cloudy, then John is happy. It is cloudy or William is drinking water. Linda is a nurse. If William drinks water, then John is happy. Can we infer the following from them? If we can, name the inference rule being used: John is not happy.
 From the fact that if Linda were a nurse, then it is late, and that Linda is a nurse we can infer that it is late via modus ponens. Finally, from the fact that if it is cloudy, then John is happy, that if William drinks water, then John is happy, and that it is cloudy or William is drinking water we can infer that John is happy via disjunction elimination, which contradicts that John is not happy. Therefore, the answer is no.