Consider the following premises. For all x_4, x_4 is not a writer. For all x_4, x_4 will drink water or x_4 will read a book. For all x_4, x_4 will drink water if and only if x_4 is a writer. Can we infer the following from them? If we can, name the inference rule being used: For all x_4, x_4 will read a book.
 From the fact that for all x_4, x_4 will drink water if and only if x_4 is a writer, and that for all x_4, x_4 is not a writer we can infer that for all x_4, x_4 will not drink water via universal biconditional elimination. Finally, from the fact that for all x_4, x_4 will drink water or x_4 will read a book, and that for all x_4, x_4 will not drink water we can infer that for all x_4, x_4 will read a book via universal disjunctive syllogism. Therefore, the answer is yes.