Consider the following premises. If it is overcast, then Jennifer is a police officer. If John reads a book, then it is overcast. If John were a carpenter, then Jennifer is a police officer. For all x_8, x_8 will read a book or x_8 is a carpenter. Can we infer the following from them? If we can, name the inference rule being used: Jennifer is a police officer.
 From the fact that for all x_8, x_8 will read a book or x_8 is a carpenter we can infer that John is reading a book or John is a carpenter via universal instantiation. From the fact that if John reads a book, then it is overcast, and that if it is overcast, then Jennifer is a police officer we can infer that if John reads a book, then Jennifer is a police officer via transitivity. Finally, from the fact that if John reads a book, then Jennifer is a police officer, that if John were a carpenter, then Jennifer is a police officer, and that John is reading a book or John is a carpenter we can infer that Jennifer is a police officer via disjunction elimination. Therefore, the answer is yes.