Consider the following premises. John is a bartender if and only if Robert is taking a plane. Robert is not taking a plane. Karen is an office clerk or John is not a bartender. John is a bartender or Karen is not an office clerk. Can we infer the following from them? If we can, name the inference rule being used: Karen is not an office clerk.
 From the fact that John is a bartender if and only if Robert is taking a plane, and that Robert is not taking a plane we can infer that John is not a bartender via biconditional elimination. From the fact that Karen is an office clerk or John is not a bartender we can infer that if John were a bartender, then Karen is an office clerk via rewriting. From the fact that John is a bartender or Karen is not an office clerk we can infer that if Karen were an office clerk, then John is a bartender via rewriting. From the fact that if Karen were an office clerk, then John is a bartender, and that if John were a bartender, then Karen is an office clerk we can infer that Karen is an office clerk if and only if John is a bartender via biconditional introduction. Finally, from the fact that Karen is an office clerk if and only if John is a bartender, and that John is not a bartender we can infer that Karen is not an office clerk via biconditional elimination. Therefore, the answer is yes.