Consider the following premises. Karen is making tea or it is not cloudy. If it is late, then it is cloudy. If Karen makes tea, then it is late. Can we infer the following from them? If we can, name the inference rule being used: If is not true that Karen is making tea if and only if it is late.
 From the fact that Karen is making tea or it is not cloudy we can infer that if it is cloudy, then Karen is making tea via rewriting. From the fact that if it is late, then it is cloudy, and that if it is cloudy, then Karen is making tea we can infer that if it is late, then Karen is making tea via transitivity. Finally, from the fact that if Karen makes tea, then it is late, and that if it is late, then Karen is making tea we can infer that Karen is making tea if and only if it is late via biconditional introduction, which contradicts that If is not true that Karen is making tea if and only if it is late. Therefore, the answer is no.