Consider the following premises. William is climbing a mountain if and only if John is reading a book. If Robert plays tennis, then William is climbing a mountain. If John reads a book, then Robert is playing tennis. Can we infer the following from them? John is reading a book if and only if William is climbing a mountain.
 From the fact that William is climbing a mountain if and only if John is reading a book we can infer that if William climbs a mountain, then John is reading a book. From the fact that if John reads a book, then Robert is playing tennis, and that if Robert plays tennis, then William is climbing a mountain we can infer that if John reads a book, then William is climbing a mountain. Finally, from the fact that if John reads a book, then William is climbing a mountain, and that if William climbs a mountain, then John is reading a book we can infer that John is reading a book if and only if William is climbing a mountain. Therefore, the answer is yes.