Consider the following premises. It is snowing or Karen is a police officer. James is fast if and only if it is snowing. Karen is a police officer if and only if James is fast. Can we infer the following from them? If we can, name the inference rule being used: James is not fast.
 From the fact that Karen is a police officer if and only if James is fast we can infer that if Karen were a police officer, then James is fast via biconditional elimination. From the fact that James is fast if and only if it is snowing we can infer that if it snows, then James is fast via biconditional elimination. Finally, from the fact that if it snows, then James is fast, that if Karen were a police officer, then James is fast, and that it is snowing or Karen is a police officer we can infer that James is fast via disjunction elimination, which contradicts that James is not fast. Therefore, the answer is no.