Consider the following premises. Patricia is drinking water. Joseph is sleeping if and only if Jennifer is excited. Jennifer is not excited. If it is late, then Joseph is sleeping. Can we infer the following from them? If we can, name the inference rule being used: It is not late and Patricia is drinking water.
 From the fact that Joseph is sleeping if and only if Jennifer is excited, and that Jennifer is not excited we can infer that Joseph is not sleeping via biconditional elimination. From the fact that if it is late, then Joseph is sleeping, and that Joseph is not sleeping we can infer that it is not late via modus tollens. Finally, from the fact that it is not late, and that Patricia is drinking water we can infer that it is not late and Patricia is drinking water via conjunction. Therefore, the answer is yes.