Consider the following premises. James is not curious. It is cloudy. James is curious if and only if Patricia is poor. Can we infer the following from them? If we can, name the inference rule being used: Patricia is not poor and it is cloudy.
 From the fact that James is curious if and only if Patricia is poor we can infer that if Patricia were poor, then James is curious via biconditional elimination. From the fact that if Patricia were poor, then James is curious, and that James is not curious we can infer that Patricia is not poor via modus tollens. Finally, from the fact that Patricia is not poor, and that it is cloudy we can infer that Patricia is not poor and it is cloudy via conjunction. Therefore, the answer is yes.