The correct hierarchy of number sets within the real number system, from largest to smallest, is:
**Rational Numbers, Integers, Whole Numbers, Natural Numbers**
This means the correct answer is the first option.
Here's a brief explanation of each:
1. **Rational Numbers**: This set includes all fractions and integers, meaning any number that can be expressed as the ratio of two integers.
2. **Integers**: This set includes all whole numbers (both positive and negative) and zero, which are still considered rational.
3. **Whole Numbers**: This set includes all natural numbers and zero, but not negative integers.
4. **Natural Numbers**: This set includes all positive whole numbers (1, 2, 3, ...).
Thus, the hierarchy from largest to smallest is: rational numbers, integers, whole numbers, natural numbers.