Consider the following premises. David is reading a book if and only if Jessica is playing tennis. William is sad if and only if Joseph is running. If David reads a book, then Joseph is running. If William were sad, then Jessica is playing tennis. Can we infer the following from them? If is not true that Jessica is playing tennis if and only if David is reading a book.
 From the fact that William is sad if and only if Joseph is running we can infer that if Joseph goes running, then William is sad. From the fact that if David reads a book, then Joseph is running, and that if Joseph goes running, then William is sad we can infer that if David reads a book, then William is sad. From the fact that if David reads a book, then William is sad, and that if William were sad, then Jessica is playing tennis we can infer that if David reads a book, then Jessica is playing tennis. From the fact that David is reading a book if and only if Jessica is playing tennis we can infer that if Jessica plays tennis, then David is reading a book. Finally, from the fact that if Jessica plays tennis, then David is reading a book, and that if David reads a book, then Jessica is playing tennis we can infer that Jessica is playing tennis if and only if David is reading a book, which contradicts that If is not true that Jessica is playing tennis if and only if David is reading a book. Therefore, the answer is no.