Consider the following premises. If Karen reads a book, then Richard is a janitor. For all y, if y works, then y is reading a book. If Richard were a janitor, then Karen is working. Can we infer the following from them? If we can, name the inference rule being used: If is not true that Richard is a janitor if and only if Karen is working.
 From the fact that for all y, if y works, then y is reading a book we can infer that if Karen works, then Karen is reading a book via universal instantiation. From the fact that if Karen works, then Karen is reading a book, and that if Karen reads a book, then Richard is a janitor we can infer that if Karen works, then Richard is a janitor via transitivity. Finally, from the fact that if Richard were a janitor, then Karen is working, and that if Karen works, then Richard is a janitor we can infer that Richard is a janitor if and only if Karen is working via biconditional introduction, which contradicts that If is not true that Richard is a janitor if and only if Karen is working. Therefore, the answer is no.