Consider the following premises. Jennifer is a musician if and only if James is rich. Mary is not cooking. James is rich if and only if Mary is a janitor. For all x_12, x_12 will cook if and only if x_12 is a janitor. Can we infer the following from them? If we can, name the inference rule being used: Jennifer is not a musician.
 From the fact that for all x_12, x_12 will cook if and only if x_12 is a janitor we can infer that Mary is cooking if and only if Mary is a janitor via universal instantiation. From the fact that Mary is cooking if and only if Mary is a janitor, and that Mary is not cooking we can infer that Mary is not a janitor via biconditional elimination. From the fact that James is rich if and only if Mary is a janitor, and that Mary is not a janitor we can infer that James is not rich via biconditional elimination. Finally, from the fact that Jennifer is a musician if and only if James is rich, and that James is not rich we can infer that Jennifer is not a musician via biconditional elimination. Therefore, the answer is yes.