Consider the following premises. If John drinks water, then William is working. William is working if and only if Karen is a politician. William is not working. If Karen were a politician, then John is drinking water. Can we infer the following from them? John is not drinking water.
 From the fact that William is working if and only if Karen is a politician we can infer that if William works, then Karen is a politician. From the fact that if William works, then Karen is a politician, and that if Karen were a politician, then John is drinking water we can infer that if William works, then John is drinking water. From the fact that if John drinks water, then William is working, and that if William works, then John is drinking water we can infer that John is drinking water if and only if William is working. Finally, from the fact that John is drinking water if and only if William is working, and that William is not working we can infer that John is not drinking water. Therefore, the answer is yes.