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