Question 17 - Examples - Chapter 1 Class 12 Relation and Functions

Last updated at August 2, 2026 by

Example 34 - Show that +, x are commutative binary, but - Whether binary commutative/associative or not

Example 34 - Chapter 1 Class 12 Relation and Functions - Part 2
Example 34 - Chapter 1 Class 12 Relation and Functions - Part 3

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Question 17 Show that + : R R R and : R R R are commutative binary operations, but : R R R and : R R R are not commutative. Addition Since a + b = b + a Hence, + is a commutative binary operation Multiplication Since a b = b a Hence, is a commutative binary operation Subtraction We have to check if a b = b a Let a = 2 , b = 5 a b = 2 5 = 3 b a = 5 2 = 3 Since a b b a Hence, is not a commutative binary operation Division : R* R* R* Here R* is all real numbers except 0 We have to check if a b = b a Let a = 2 , b = 5 a b = = 2 5 b a = = 5 2 Since a b b a Hence, is not a commutative binary operation

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