Consider the following premises. For all x_8, x_8 is a politician. For all x_8, x_8 is a politician if and only if x_8 will read a book. For all x_8, x_8 will take a plane. 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 will not read a book.
 From the fact that for all x_8, x_8 is a politician if and only if x_8 will read a book we can infer that for all x_8, if x_8 were a politician, then x_8 is reading a book via universal biconditional elimination. From the fact that for all x_8, x_8 is a politician, and that for all x_8, x_8 will take a plane we can infer that for all x_8, x_8 is a politician and x_8 will take a plane via universal conjunction. From the fact that for all x_8, x_8 is a politician and x_8 will take a plane we can infer that for all x_8, x_8 is a politician via universal simplification. Finally, from the fact that for all x_8, if x_8 were a politician, then x_8 is reading a book, and that for all x_8, x_8 is a politician we can infer that for all x_8, x_8 will read a book via universal modus ponens, which contradicts that There is at least one x_8 for which x_8 will not read a book. Therefore, the answer is no.