Consider the following premises. For all x, if x cooks, then x is sleeping. For all x, x will cook or x will drive a car. For all x, x will read a book if and only if x will drive a car. For all x, if x sleeps, then x is reading a book. Can we infer the following from them? There is at least one x for which x will not read a book.
 From the fact that for all x, if x cooks, then x is sleeping, and that for all x, if x sleeps, then x is reading a book we can infer that for all x, if x cooks, then x is reading a book. From the fact that for all x, x will read a book if and only if x will drive a car we can infer that for all x, if x drives a car, then x is reading a book. Finally, from the fact that for all x, if x cooks, then x is reading a book, that for all x, if x drives a car, then x is reading a book, and that for all x, x will cook or x will drive a car we can infer that for all x, x will read a book, which contradicts that There is at least one x for which x will not read a book. Therefore, the answer is no.