Answer
No such book can exist. Attempting to construct one leads to a logical contradiction due to self-reference.
This is a paradox of **self-inclusion** — and shows the limits of naive self-reference in formal systems.
Work Step by Step
### Problem:
**Can there exist a book that refers to all those books and only those books that do not refer to themselves?**
---
### ✅ Short Answer:
\[
\boxed{\text{No, such a book cannot exist.}}
\]
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### 🧠 Explanation: This is a **version of Russell’s Paradox**.
Let’s suppose such a book **B** exists.
Book **B** contains a list of **all books that do not refer to themselves**.
Now ask the key question:
> **Does book B refer to itself?**
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### ❗ Case 1: B **does** refer to itself.
Then B refers to a book that refers to itself → which it’s **not supposed to list**.
**Contradiction.**
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### ❗ Case 2: B **does not** refer to itself.
Then B satisfies the condition of books that **do not** refer to themselves → so it **should be in its own list**.
But that would mean it **does** refer to itself.
**Contradiction again.**
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### 🔁 This loop is exactly the structure of **Russell's Paradox**:
> Let R be the set of all sets that do not contain themselves.
> Does R contain itself?
