Give three examples each to show that the whole numbers are:
not commutative under subtraction.

Answer

To show that whole numbers are not commutative under subtraction, we will provide three examples. The commutative property states that for any two numbers \( a \) and \( b \), \( a - b \) should equal \( b - a \). However, this is not the case with subtraction. Let's go through the examples step by step.

### Example 1:
1. **Choose two whole numbers:** Let \( a = 15 \) and \( b = 7 \).
2. **Calculate \( a - b \):**
\[ 15 - 7 = 8 \]
3. **Calculate \( b - a \):**
\[ 7 - 15 = -8 \]
4. **Conclusion:** Since \( 15 - 7 \neq 7 - 15 \) (8 is not equal to -8), this shows that subtraction is not commutative.

### Example 2:
1. **Choose two whole numbers:** Let \( a = 30 \) and \( b = 14 \).
2. **Calculate \( a - b \):**
\[ 30 - 14 = 16 \]
3. **Calculate \( b - a \):**
\[ 14 - 30 = -16 \]
4. **Conclusion:** Since \( 30 - 14 \neq 14 - 30 \) (16 is not equal to -16), this demonstrates that subtraction is not commutative.

### Example 3:
1. **Choose two whole numbers:** Let \( a = 50 \) and \( b = 15 \).
2. **Calculate \( a - b \):**
\[ 50 - 15 = 35 \]
3. **Calculate \( b - a \):**
\[ 15 - 50 = -35 \]
4. **Conclusion:** Since \( 50 - 15 \neq 15 - 50 \) (35 is not equal to -35), this further confirms that subtraction is not commutative.

### Summary:
From the three examples, we can conclude that whole numbers are not commutative under subtraction because \( a - b \) does not equal \( b - a \).