Consider the following premises. For all y_1, y_1 is a politician. If David doesn't go running, then it is cloudy. David is running if and only if Barbara is a doctor. Barbara is not a doctor. Can we infer the following from them? It is not cloudy.
 From the fact that David is running if and only if Barbara is a doctor, and that Barbara is not a doctor we can infer that David is not running. Finally, from the fact that if David doesn't go running, then it is cloudy, and that David is not running we can infer that it is cloudy, which contradicts that It is not cloudy. Therefore, the answer is no.