Consider the following premises. It is overcast. Jennifer is not sad. If Joseph cooks, then it is not overcast. For all y, y will play tennis if and only if y is sad. Can we infer the following from them? If we can, name the inference rule being used: Jennifer is not playing tennis and Joseph is not cooking.
 From the fact that if Joseph cooks, then it is not overcast, and that it is overcast we can infer that Joseph is not cooking via modus tollens. From the fact that for all y, y will play tennis if and only if y is sad we can infer that Jennifer is playing tennis if and only if Jennifer is sad via universal instantiation. From the fact that Jennifer is playing tennis if and only if Jennifer is sad, and that Jennifer is not sad we can infer that Jennifer is not playing tennis via biconditional elimination. Finally, from the fact that Jennifer is not playing tennis, and that Joseph is not cooking we can infer that Jennifer is not playing tennis and Joseph is not cooking via conjunction. Therefore, the answer is yes.