Consider the following premises. It is raining or Charles is not taking a plane. If Mary were a writer, then Charles is taking a plane. It is raining if and only if Mary is a writer. Can we infer the following from them? If we can, name the inference rule being used: If is not true that it is raining if and only if Charles is taking a plane.
 From the fact that it is raining or Charles is not taking a plane we can infer that if Charles takes a plane, then it is raining via rewriting. From the fact that it is raining if and only if Mary is a writer we can infer that if it rains, then Mary is a writer via biconditional elimination. From the fact that if it rains, then Mary is a writer, and that if Mary were a writer, then Charles is taking a plane we can infer that if it rains, then Charles is taking a plane via transitivity. Finally, from the fact that if it rains, then Charles is taking a plane, and that if Charles takes a plane, then it is raining we can infer that it is raining if and only if Charles is taking a plane via biconditional introduction, which contradicts that If is not true that it is raining if and only if Charles is taking a plane. Therefore, the answer is no.