Consider the following premises. For all x_8, x_8 will not play squash. For all x_8, x_8 will read a book or x_8 is a sailor. For all x_8, x_8 will play squash if and only if x_8 will read a book. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_8 for which x_8 is not a sailor.
 From the fact that for all x_8, x_8 will play squash if and only if x_8 will read a book we can infer that for all x_8, if x_8 reads a book, then x_8 is playing squash via universal biconditional elimination. From the fact that for all x_8, if x_8 reads a book, then x_8 is playing squash, and that for all x_8, x_8 will not play squash we can infer that for all x_8, x_8 will not read a book via universal modus tollens. Finally, from the fact that for all x_8, x_8 will read a book or x_8 is a sailor, and that for all x_8, x_8 will not read a book we can infer that for all x_8, x_8 is a sailor via universal disjunctive syllogism, which contradicts that There is at least one x_8 for which x_8 is not a sailor. Therefore, the answer is no.