To solve the question of selecting the incorrect option, we will analyze each option step by step.
### Step 1: Analyze Option A
**Statement:** The smallest 4-digit number having 3 different digits is 1002.
- The smallest 4-digit number is 1000.
- The next numbers are 1001, 1002, 1003, etc.
- 1000 has 2 different digits (1 and 0).
- 1001 has 2 different digits (1 and 0).
- 1002 has 3 different digits (1, 0, and 2).
**Conclusion:** This statement is true since 1002 is indeed the smallest 4-digit number with 3 different digits.
**Hint:** Check the definition of a 4-digit number and count the unique digits.
### Step 2: Analyze Option B
**Statement:** Whole numbers are always commutative under addition and multiplication.
- The commutative property states that changing the order of the numbers does not change the sum or product.
- For example, \( a + b = b + a \) and \( a \times b = b \times a \) for whole numbers.
**Conclusion:** This statement is true.
**Hint:** Recall the commutative property and test it with simple whole numbers.
### Step 3: Analyze Option C
**Statement:** All whole numbers are natural numbers.
- Whole numbers include 0, 1, 2, 3, etc.
- Natural numbers start from 1 (1, 2, 3, ...).
- Therefore, 0 is a whole number but not a natural number.
**Conclusion:** This statement is false because not all whole numbers are natural numbers.
**Hint:** Define whole numbers and natural numbers and identify the difference.
### Step 4: Analyze Option D
**Statement:** The number is divisible by 11.
- To check divisibility by 11, we find the difference between the sum of the digits in odd positions and the sum of the digits in even positions.
- If the difference is 0 or divisible by 11, then the number is divisible by 11.
**Conclusion:** This statement is true based on the calculations provided.
**Hint:** Use the divisibility rule for 11 and apply it to the digits of the number.
### Final Conclusion
After analyzing all the options, we find that:
- Option A: True
- Option B: True
- Option C: **False** (this is the incorrect option)
- Option D: True
Thus, the incorrect option is **C**.
