Consider the following premises. David is taking a plane if and only if Susan is a writer. If David goes running, then Susan is a writer. David is taking a plane if and only if David is running. Can we infer the following from them? If is not true that Susan is a writer if and only if David is taking a plane.
 From the fact that David is taking a plane if and only if David is running we can infer that if David takes a plane, then David is running. From the fact that if David takes a plane, then David is running, and that if David goes running, then Susan is a writer we can infer that if David takes a plane, then Susan is a writer. From the fact that David is taking a plane if and only if Susan is a writer we can infer that if Susan were a writer, then David is taking a plane. Finally, from the fact that if Susan were a writer, then David is taking a plane, and that if David takes a plane, then Susan is a writer we can infer that Susan is a writer if and only if David is taking a plane, which contradicts that If is not true that Susan is a writer if and only if David is taking a plane. Therefore, the answer is no.