Which one of the following statements is not true for integers?

Options

A. Division is commutative.
B. 1 is the multiplicative identity.
C. Subtraction is not commutative.
D. Multiplication is associative.

Answer

To determine which statement is not true for integers, we will analyze the properties of integers step by step.

### Step 1: Understand the properties of operations on integers

1. **Commutative Property**: This property states that the order in which two numbers are added or multiplied does not change the result. For example:
- Addition: \( A + B = B + A \)
- Multiplication: \( A \times B = B \times A \)

2. **Division**: This operation is not commutative. For example:
- \( 4 \div 2 \neq 2 \div 4 \)
- Thus, division does not satisfy the commutative property.

### Step 2: Analyze the statements given

1. **Division is commutative**: As established, this statement is **not true** for integers.
2. **Multiplicative identity**: The multiplicative identity for integers is 1, as \( A \times 1 = A \). This statement is **true**.
3. **Subtraction is not commutative**: For example, \( A - B \neq B - A \). This statement is **true**.
4. **Multiplication is associative**: This means that \( (A \times B) \times C = A \times (B \times C \). This statement is **true**.

### Step 3: Conclusion

From the analysis, the statement that is **not true** for integers is:
- **Division is commutative**.

### Final Answer:
The statement that is not true for integers is: **Division is commutative**.

---