Consider the following premises. It is raining if and only if Sarah is cooking. It is not raining. It is not cloudy. It is cloudy or Richard is excited. Can we infer the following from them? Sarah is cooking.
 From the fact that it is cloudy or Richard is excited, and that it is not cloudy we can infer that Richard is excited. Finally, from the fact that it is raining if and only if Sarah is cooking, and that it is not raining we can infer that Sarah is not cooking, which contradicts that Sarah is cooking. Therefore, the answer is no.