Consider the following premises. If it is cold, then Barbara is writing a letter. It is cold. If Barbara writes a letter, then it is overcast. Can we infer the following from them? If we can, name the inference rule being used: It is overcast or James is reading a book.
 From the fact that if it is cold, then Barbara is writing a letter, and that it is cold we can infer that Barbara is writing a letter via modus ponens. From the fact that if Barbara writes a letter, then it is overcast, and that Barbara is writing a letter we can infer that it is overcast via modus ponens. Finally, from the fact that it is overcast we can infer that it is overcast or James is reading a book via addition. Therefore, the answer is yes.