Consider the following premises. Richard is a politician. It is raining if and only if it is snowing. If it is cloudy, then Richard is not a politician. If it snows, then it is cloudy. Can we infer the following from them? If we can, name the inference rule being used: It is raining.
 From the fact that if it is cloudy, then Richard is not a politician, and that Richard is a politician we can infer that it is not cloudy via modus tollens. From the fact that if it snows, then it is cloudy, and that it is not cloudy we can infer that it is not snowing via modus tollens. Finally, from the fact that it is raining if and only if it is snowing, and that it is not snowing we can infer that it is not raining via biconditional elimination, which contradicts that It is raining. Therefore, the answer is no.