Consider the following premises. If James were a scientist, then William is sleeping. Patricia is reading a book if and only if it is windy. If it is windy, then William is sleeping. James is a scientist or Patricia is reading a book. Can we infer the following from them? If we can, name the inference rule being used: William is not sleeping.
 From the fact that Patricia is reading a book if and only if it is windy we can infer that if Patricia reads a book, then it is windy via biconditional elimination. From the fact that if Patricia reads a book, then it is windy, and that if it is windy, then William is sleeping we can infer that if Patricia reads a book, then William is sleeping via transitivity. Finally, from the fact that if James were a scientist, then William is sleeping, that if Patricia reads a book, then William is sleeping, and that James is a scientist or Patricia is reading a book we can infer that William is sleeping via disjunction elimination, which contradicts that William is not sleeping. Therefore, the answer is no.