Consider the following premises. Elisabeth is not bored. David is playing tennis if and only if Elisabeth is bored. David is playing tennis if and only if Barbara is a cashier. Can we infer the following from them? If we can, name the inference rule being used: Barbara is a cashier.
 From the fact that David is playing tennis if and only if Elisabeth is bored we can infer that if David plays tennis, then Elisabeth is bored via biconditional elimination. From the fact that if David plays tennis, then Elisabeth is bored, and that Elisabeth is not bored we can infer that David is not playing tennis via modus tollens. Finally, from the fact that David is playing tennis if and only if Barbara is a cashier, and that David is not playing tennis we can infer that Barbara is not a cashier via biconditional elimination, which contradicts that Barbara is a cashier. Therefore, the answer is no.