Consider the following premises. If it is late, then it is windy. If James cooks, then it is late. If it is windy, then Sarah is a politician. James is cooking or Sarah is not a politician. Can we infer the following from them? If we can, name the inference rule being used: If is not true that Sarah is a politician if and only if James is cooking.
 From the fact that if it is late, then it is windy, and that if it is windy, then Sarah is a politician we can infer that if it is late, then Sarah is a politician via transitivity. From the fact that if James cooks, then it is late, and that if it is late, then Sarah is a politician we can infer that if James cooks, then Sarah is a politician via transitivity. From the fact that James is cooking or Sarah is not a politician we can infer that if Sarah were a politician, then James is cooking via rewriting. Finally, from the fact that if Sarah were a politician, then James is cooking, and that if James cooks, then Sarah is a politician we can infer that Sarah is a politician if and only if James is cooking via biconditional introduction, which contradicts that If is not true that Sarah is a politician if and only if James is cooking. Therefore, the answer is no.