If a property holds for whole numbers, then it also holds for _______ .

Options

A. Rational numbers
B. Natural numbers
C. Integers
D. Both A and C

Answer

To solve the question "If a property holds for whole numbers, then it also holds for _______," we need to analyze the relationship between whole numbers and the other types of numbers given in the options.

### Step-by-Step Solution:

1. **Identify the Types of Numbers:**
- Whole numbers include all non-negative integers: 0, 1, 2, 3, ...
- Natural numbers are the counting numbers: 1, 2, 3, ...
- Integers include all whole numbers and their negative counterparts: ..., -3, -2, -1, 0, 1, 2, 3, ...
- Rational numbers include all numbers that can be expressed as a fraction of two integers, which includes integers, whole numbers, and natural numbers.

2. **Understanding the Property:**
- If a property holds for whole numbers, it means that any statement or rule that is true for whole numbers must also be examined for the other types of numbers.

3. **Analyzing the Options:**
- **Natural Numbers:** Since natural numbers do not include zero, a property that involves zero (like "0 is a whole number") would not hold for natural numbers.
- **Integers:** Since integers include all whole numbers and also negative numbers, any property that holds for whole numbers will also hold for integers.
- **Rational Numbers:** Since rational numbers include all integers (and hence all whole numbers), any property that holds for whole numbers will also hold for rational numbers.

4. **Conclusion:**
- The property that holds for whole numbers will also hold true for integers and rational numbers. Therefore, the correct answer is both A (rational numbers) and C (integers).

5. **Final Answer:**
- If a property holds for whole numbers, then it also holds for **both A and C** (rational numbers and integers).