Consider the following premises. For all x, if x cooks, then x is drinking water. For all x, if x were a politician, then x is reading a book. For all x, if x drinks water, then x is a politician. For all x, if x reads a book, then x is cooking. Can we infer the following from them? There is at least one x for which if is not true that x is a politician if and only if x will drink water.
 From the fact that for all x, if x were a politician, then x is reading a book, and that for all x, if x reads a book, then x is cooking we can infer that for all x, if x were a politician, then x is cooking. From the fact that for all x, if x were a politician, then x is cooking, and that for all x, if x cooks, then x is drinking water we can infer that for all x, if x were a politician, then x is drinking water. Finally, from the fact that for all x, if x were a politician, then x is drinking water, and that for all x, if x drinks water, then x is a politician we can infer that for all x, x is a politician if and only if x will drink water, which contradicts that There is at least one x for which if is not true that x is a politician if and only if x will drink water. Therefore, the answer is no.