Consider the following premises. Jessica is a doctor. Jessica is a doctor if and only if it is late. Barbara is working if and only if it is late. Can we infer the following from them? If we can, name the inference rule being used: It is not late.
 From the fact that Barbara is working if and only if it is late we can infer that if Barbara works, then it is late via biconditional elimination. From the fact that Jessica is a doctor we can infer that Jessica is a doctor or Barbara is working via addition. From the fact that Jessica is a doctor if and only if it is late we can infer that if Jessica were a doctor, then it is late via biconditional elimination. Finally, from the fact that if Jessica were a doctor, then it is late, that if Barbara works, then it is late, and that Jessica is a doctor or Barbara is working we can infer that it is late via disjunction elimination, which contradicts that It is not late. Therefore, the answer is no.