Consider the following premises. Joseph is not reading a book. If it is sunny, then Joseph is reading a book. If Michael works, then it is sunny. If Joseph reads a book, then Michael is working. Can we infer the following from them? If we can, name the inference rule being used: Michael is working.
 From the fact that if Michael works, then it is sunny, and that if it is sunny, then Joseph is reading a book we can infer that if Michael works, then Joseph is reading a book via transitivity. From the fact that if Michael works, then Joseph is reading a book, and that if Joseph reads a book, then Michael is working we can infer that Michael is working if and only if Joseph is reading a book via biconditional introduction. Finally, from the fact that Michael is working if and only if Joseph is reading a book, and that Joseph is not reading a book we can infer that Michael is not working via biconditional elimination, which contradicts that Michael is working. Therefore, the answer is no.