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JAMB Mathematics 2008 Question 21

Question 21

Binary Operations

A binary operation * defined on the set of positive integers is such that x * y = 2x − 3y + 2 for all positive integers x and y. The binary operation is

  1. A.commutative and closed on the set of positive integers
  2. B.neither commutative nor closed on the set of positive integers
  3. C.commutative but not closed on the set of positive integers
  4. D.not commutative but closed on the set of positive integers.
Show the answer and explanation

Answer: B (neither commutative nor closed on the set of positive integers)

Explanation

y * x = 2y − 3x + 2 is different from x * y, so it is not commutative. 1 * 2 = 2 − 6 + 2 = −2 is not a positive integer, so it is not closed.