Consider the following premises. John is reading a book or Mary is not climbing a mountain. Elisabeth is not taking a plane. John is reading a book if and only if Elisabeth is taking a plane. Can we infer the following from them? If we can, name the inference rule being used: Mary is climbing a mountain.
 From the fact that John is reading a book if and only if Elisabeth is taking a plane, and that Elisabeth is not taking a plane we can infer that John is not reading a book via biconditional elimination. From the fact that John is reading a book or Mary is not climbing a mountain we can infer that if Mary climbs a mountain, then John is reading a book via rewriting. Finally, from the fact that if Mary climbs a mountain, then John is reading a book, and that John is not reading a book we can infer that Mary is not climbing a mountain via modus tollens, which contradicts that Mary is climbing a mountain. Therefore, the answer is no.