Consider the following premises. If it is cold, then Jessica is drinking water. It is cold or it is cloudy. It is raining. Jessica is drinking water or it is not cloudy. Can we infer the following from them? If we can, name the inference rule being used: Jessica is drinking water and it is raining.
 From the fact that Jessica is drinking water or it is not cloudy we can infer that if it is cloudy, then Jessica is drinking water via rewriting. From the fact that if it is cold, then Jessica is drinking water, that if it is cloudy, then Jessica is drinking water, and that it is cold or it is cloudy we can infer that Jessica is drinking water via disjunction elimination. Finally, from the fact that Jessica is drinking water, and that it is raining we can infer that Jessica is drinking water and it is raining via conjunction. Therefore, the answer is yes.