Consider the following premises. It is raining if and only if John is drinking water. Elisabeth is not playing a game. Elisabeth is playing a game or John is drinking water. Can we infer the following from them? It is raining.
 From the fact that it is raining if and only if John is drinking water we can infer that if John drinks water, then it is raining. From the fact that Elisabeth is playing a game or John is drinking water, and that Elisabeth is not playing a game we can infer that John is drinking water. Finally, from the fact that if John drinks water, then it is raining, and that John is drinking water we can infer that it is raining. Therefore, the answer is yes.