Which of the following binary operations on the set of natural numbers is commutative?
Which of the following binary operations on the set of natural numbers is commutative?
- A. a ∗ b = a − b
- B. a ∗ b = a ÷ b
- C. a ∗ b = a + b + ab
- D. a ∗ b = aᵇ
Answer: C) a ∗ b = a + b + ab
Explanation: a + b + ab = b + a + ba, so commutative. Others: a − b ≠ b − a; a ÷ b ≠ b ÷ a; aᵇ ≠ bᵃ in general.
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