Consider the following premises. Sarah is playing a game. Barbara is drinking water if and only if Sarah is a writer. For all y, y is not a writer. Can we infer the following from them? Barbara is not drinking water.
 From the fact that for all y, y is not a writer we can infer that Sarah is not a writer. Finally, from the fact that Barbara is drinking water if and only if Sarah is a writer, and that Sarah is not a writer we can infer that Barbara is not drinking water. Therefore, the answer is yes.