Let \( A=\left\{-7,-\frac{20}{4},-\frac{5}{8},-\sqrt{13}, 0, \frac{1}{4}, 2,4 x, 5, \sqrt{8}\right\} \). List all the elements of \( A \) that belong to the set of natural numbers

To determine which elements of the set \( A = \left\{-7, -\frac{20}{4}, -\frac{5}{8}, -\sqrt{13}, 0, \frac{1}{4}, 2, 4x, 5, \sqrt{8}\right\} \) belong to the set of natural numbers, let's analyze each element individually. **Natural Numbers Definition:** Natural numbers are the set of positive integers starting from 1, i.e., \( \mathbb{N} = \{1, 2, 3, \ldots\} \). **Analyzing Each Element:** 1. **\(-7\):** This is a negative integer. Natural numbers are positive, so \(-7\) is **not** a natural number. 2. **\(-\frac{20}{4}\):** Simplifies to \(-5\), which is a negative integer. Hence, **not** a natural number. 3. **\(-\frac{5}{8}\):** A negative fraction. **Not** a natural number. 4. **\(-\sqrt{13}\):** A negative irrational number. **Not** a natural number. 5. **\(0\):** Zero is not typically included in the set of natural numbers. **Not** a natural number. 6. **\(\frac{1}{4}\):** A positive fraction, but not an integer. **Not** a natural number. 7. **\(2\):** This is a positive integer. **Yes**, it is a natural number. 8. **\(4x\):** This term involves a variable \(x\). Without additional information about \(x\), we cannot determine if \(4x\) is a natural number. Assuming \(x\) is an integer, but since it's not specified, we'll exclude this from our list of definite natural numbers. 9. **\(5\):** This is a positive integer. **Yes**, it is a natural number. 10. **\(\sqrt{8}\):** An irrational number (approximately 2.828). **Not** a natural number. **Conclusion:** The elements of \( A \) that are natural numbers are: \[ 2 \quad \text{and} \quad 5 \] **Final Answer:** \[ 2 \quad \text{and} \quad 5 \]