Consider the following premises. For all x, x will drink water if and only if x is sad. For all x, if x were sad, then x is a writer. Can we infer the following from them? There is at least one x for which the fact that x drinks water does not imply that x is a writer.
 From the fact that for all x, x will drink water if and only if x is sad we can infer that for all x, if x drinks water, then x is sad. Finally, from the fact that for all x, if x drinks water, then x is sad, and that for all x, if x were sad, then x is a writer we can infer that for all x, if x drinks water, then x is a writer, which contradicts that There is at least one x for which the fact that x drinks water does not imply that x is a writer. Therefore, the answer is no.