Consider the following premises. Linda is a carpenter or Elisabeth is not an astronaut. If Mary reads a book, then Joseph is taking a plane. Joseph is not taking a plane. If Joseph takes a plane, then Mary is reading a book. Mary is reading a book if and only if Linda is a carpenter. Can we infer the following from them? If we can, name the inference rule being used: Elisabeth is not an astronaut.
 From the fact that Linda is a carpenter or Elisabeth is not an astronaut we can infer that if Elisabeth were an astronaut, then Linda is a carpenter via rewriting. From the fact that if Joseph takes a plane, then Mary is reading a book, and that if Mary reads a book, then Joseph is taking a plane we can infer that Joseph is taking a plane if and only if Mary is reading a book via biconditional introduction. From the fact that Joseph is taking a plane if and only if Mary is reading a book, and that Joseph is not taking a plane we can infer that Mary is not reading a book via biconditional elimination. From the fact that Mary is reading a book if and only if Linda is a carpenter, and that Mary is not reading a book we can infer that Linda is not a carpenter via biconditional elimination. Finally, from the fact that if Elisabeth were an astronaut, then Linda is a carpenter, and that Linda is not a carpenter we can infer that Elisabeth is not an astronaut via modus tollens. Therefore, the answer is yes.