Consider the following premises. It is cloudy if and only if it is raining. If Richard drinks water, then Elisabeth is not taking a plane. It is cloudy if and only if Sarah is a carpenter. Elisabeth is taking a plane. Sarah is not a carpenter. Can we infer the following from them? If we can, name the inference rule being used: Richard is not drinking water and it is not raining.
 From the fact that if Richard drinks water, then Elisabeth is not taking a plane, and that Elisabeth is taking a plane we can infer that Richard is not drinking water via modus tollens. From the fact that it is cloudy if and only if Sarah is a carpenter, and that Sarah is not a carpenter we can infer that it is not cloudy via biconditional elimination. From the fact that it is cloudy if and only if it is raining, and that it is not cloudy we can infer that it is not raining via biconditional elimination. Finally, from the fact that Richard is not drinking water, and that it is not raining we can infer that Richard is not drinking water and it is not raining via conjunction. Therefore, the answer is yes.