Consider the following premises. It is sunny or Patricia is reading a book. If it is sunny, then Linda is making tea. If Patricia reads a book, then it is cloudy. If Linda makes tea, then it is cloudy. Can we infer the following from them? If we can, name the inference rule being used: It is not cloudy.
 From the fact that if it is sunny, then Linda is making tea, and that if Linda makes tea, then it is cloudy we can infer that if it is sunny, then it is cloudy via transitivity. Finally, from the fact that if it is sunny, then it is cloudy, that if Patricia reads a book, then it is cloudy, and that it is sunny or Patricia is reading a book we can infer that it is cloudy via disjunction elimination, which contradicts that It is not cloudy. Therefore, the answer is no.