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