Consider the following premises. Karen is sleeping if and only if it is sunny. If James cooks, then Karen is sleeping. James is cooking. Can we infer the following from them? If we can, name the inference rule being used: It is not sunny.
 From the fact that Karen is sleeping if and only if it is sunny we can infer that if Karen sleeps, then it is sunny via biconditional elimination. From the fact that if James cooks, then Karen is sleeping, and that James is cooking we can infer that Karen is sleeping via modus ponens. Finally, from the fact that if Karen sleeps, then it is sunny, and that Karen is sleeping we can infer that it is sunny via modus ponens, which contradicts that It is not sunny. Therefore, the answer is no.