Let a binary operation ‘ × ‘ be defined on a set A. The operation will be commutative if

JAMB Mathematics 2023 57 views

Let a binary operation ‘ × ‘ be defined on a set A. The operation will be commutative if

  1. (a × b) × c = a × (b × c)
  2. (b o c) × a = (b × a) o (c × a)
  3. a × b = b × a ✓
  4. None of the above

Explanation

A binary operation is commutative when the order of elements does not matter. This means performing the operation on a then b gives the same result as performing it on b then a. The mathematical definition is a × b equals b × a.

For example, addition is commutative because 3 plus 5 equals 5 plus 3 equals 8. Multiplication is also commutative because 4 times 7 equals 7 times 4 equals 28. Order does not change the result.

The first option describes the associative property, not commutative. The second option describes distributive property. Only the third option correctly defines when elements can be swapped without changing the result, which is commutativity.

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