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

2019

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

  1. A.

    Multiplication is associative.

  2. B.

    Division is commutative.

  3. C.

    1 is the multiplicative identity.

  4. D.

    Subtraction is not commutative.

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Correct answer: B

To determine which statement is not true for integers, we evaluate each property. Multiplication of integers is associative, meaning (a × b) × c = a × (b × c), so Option A is true. The number 1 acts as the multiplicative identity because multiplying any integer by 1 leaves it unchanged, making Option C true. Subtraction is not commutative since changing the order changes the result (e.g., 5 - 3 ≠ 3 - 5), confirming Option D is true. However, division is not commutative for integers; swapping the dividend and divisor changes the quotient (e.g., 6 ÷ 2 = 3, but 2 ÷ 6 is not an integer). Therefore, the statement that division is commutative is false. Option B is the correct answer.

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