Question 19 - Examples - Chapter 1 Class 12 Relation and Functions

Last updated at July 31, 2026 by

Example 36 - Show addition, multiplication are associative on R - Whether binary commutative/associative or not

Example 36 - Chapter 1 Class 12 Relation and Functions - Part 2
Example 36 - Chapter 1 Class 12 Relation and Functions - Part 3 Example 36 - Chapter 1 Class 12 Relation and Functions - Part 4

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Question 19 Show that addition and multiplication are associative binary operation on R. But subtraction is not associative on R. Division is not associative on R∗. Addition * is associative if (a * b) * c = a * (b * c) Since (a * b) * c = a * (b * c) ∀ a, b, c ∈ R + is an associative binary operation Multiplication * is associative if (a * b) * c = a * (b * c) Since (a * b) * c = a * (b * c) ∀ a, b, c ∈ R × is an associative binary operation Subtraction * is associative if (a * b) * c = a * (b * c) Since (a * b) * c ≠ a * (b * c) ∀ a, b, c ∈ R – is not an associative binary operation Division * is associative if (a * b) * c = a * (b * c) Since (a * b) * c ≠ a * (b * c) ÷ is not an associative binary operation

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