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