Consider the following premises. If it is not overcast, then it is cold. It is cloudy. It is overcast if and only if Karen is reading a book. Karen is not reading a book. Can we infer the following from them? If we can, name the inference rule being used: It is not cold.
 From the fact that it is overcast if and only if Karen is reading a book, and that Karen is not reading a book we can infer that it is not overcast via biconditional elimination. Finally, from the fact that if it is not overcast, then it is cold, and that it is not overcast we can infer that it is cold via modus ponens, which contradicts that It is not cold. Therefore, the answer is no.