Consider the following premises. If it is cloudy, then James is a police officer. If it is cloudy, then David is sad. James is not a police officer. If David were sad, then Sarah is drinking water. If Sarah drinks water, then it is cloudy. Can we infer the following from them? If we can, name the inference rule being used: David is sad.
 From the fact that if it is cloudy, then James is a police officer, and that James is not a police officer we can infer that it is not cloudy via modus tollens. From the fact that if David were sad, then Sarah is drinking water, and that if Sarah drinks water, then it is cloudy we can infer that if David were sad, then it is cloudy via transitivity. From the fact that if it is cloudy, then David is sad, and that if David were sad, then it is cloudy we can infer that it is cloudy if and only if David is sad via biconditional introduction. Finally, from the fact that it is cloudy if and only if David is sad, and that it is not cloudy we can infer that David is not sad via biconditional elimination, which contradicts that David is sad. Therefore, the answer is no.