Consider the following premises. David is a doctor if and only if it is late. If David were a cashier, then it is late. David is not a doctor. David is a cashier or Jennifer is a police officer. Can we infer the following from them? If we can, name the inference rule being used: Jennifer is a police officer.
 From the fact that David is a doctor if and only if it is late we can infer that if it is late, then David is a doctor via biconditional elimination. From the fact that if it is late, then David is a doctor, and that David is not a doctor we can infer that it is not late via modus tollens. From the fact that if David were a cashier, then it is late, and that it is not late we can infer that David is not a cashier via modus tollens. Finally, from the fact that David is a cashier or Jennifer is a police officer, and that David is not a cashier we can infer that Jennifer is a police officer via disjunctive syllogism. Therefore, the answer is yes.