Consider the following premises. Barbara is drinking water. For all x, x will drink water or x will not cook. For all x, if x drinks water, then x is cooking. Can we infer the following from them? For all x, x will not cook.
 From the fact that Barbara is drinking water we can infer that there is at least one x for which x will drink water. From the fact that for all x, x will drink water or x will not cook we can infer that for all x, if x cooks, then x is drinking water. From the fact that for all x, if x drinks water, then x is cooking, and that for all x, if x cooks, then x is drinking water we can infer that for all x, x will drink water if and only if x will cook. From the fact that for all x, x will drink water if and only if x will cook we can infer that for all x, if x drinks water, then x is cooking. Finally, from the fact that for all x, if x drinks water, then x is cooking, and that there is at least one x for which x will drink water we can infer that there is at least one x for which x will cook, which contradicts that For all x, x will not cook. Therefore, the answer is no.