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JAMB Mathematics 1995 Question 21

Question 21

Binary Operations

Which of the following binary operations is commutative in the set of integers?

  1. A.a*b = a + 2b
  2. B.a*b = a + b − ab
  3. C.a*b = a2 + b
  4. D.a*b = a(b + 1)/2
Show the answer and explanation

Answer: B (a*b = a + b − ab)

Explanation

Commutative means a*b = b*a. Swapping a and b in a + b − ab gives b + a − ba, which is the same. The others change, e.g. 1 + 2(2) ≠ 2 + 2(1).