imo class 12 relations and functions

Which of the following binary operations on Z is not closed?

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Which of the following binary operations on Z is not closed?

  • A. a ∗ b = a + b
  • B. a ∗ b = a − b
  • C. a ∗ b = a × b
  • D. a ∗ b = a ÷ b

Answer: D) a ∗ b = a ÷ b

Explanation: Division of integers is not always an integer (e.g., 3 ÷ 2 = 1.5 ∉ Z). Addition, subtraction, and multiplication are closed on Z.

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