Consider the following premises. If Thomas cooks, then Karen is reading a book. If Thomas cooks, then Karen is reading a book. Karen is reading a book if and only if Thomas is cooking. Can we infer the following from them? Thomas is cooking if and only if Karen is reading a book.
 From the fact that Karen is reading a book if and only if Thomas is cooking we can infer that if Karen reads a book, then Thomas is cooking. Finally, from the fact that if Thomas cooks, then Karen is reading a book, and that if Karen reads a book, then Thomas is cooking we can infer that Thomas is cooking if and only if Karen is reading a book. Therefore, the answer is yes.