Consider the following premises. Karen is not listening to a song. For all x, x will listen to a song if and only if x will read a book. Karen is reading a book if and only if Mary is cooking. Can we infer the following from them? If we can, name the inference rule being used: Mary is not cooking.
 From the fact that for all x, x will listen to a song if and only if x will read a book we can infer that Karen is listening to a song if and only if Karen is reading a book via universal instantiation. From the fact that Karen is listening to a song if and only if Karen is reading a book, and that Karen is not listening to a song we can infer that Karen is not reading a book via biconditional elimination. Finally, from the fact that Karen is reading a book if and only if Mary is cooking, and that Karen is not reading a book we can infer that Mary is not cooking via biconditional elimination. Therefore, the answer is yes.