Consider the following premises. Sarah is happy if and only if Mary is driving a car. Mary is not driving a car. Sarah is happy if and only if Joseph is listening to a song. Can we infer the following from them? If we can, name the inference rule being used: Joseph is listening to a song.
 From the fact that Sarah is happy if and only if Mary is driving a car, and that Mary is not driving a car we can infer that Sarah is not happy via biconditional elimination. Finally, from the fact that Sarah is happy if and only if Joseph is listening to a song, and that Sarah is not happy we can infer that Joseph is not listening to a song via biconditional elimination, which contradicts that Joseph is listening to a song. Therefore, the answer is no.