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Question 17 - Whether binary commutative/associative or not - Chapter 1 Class 12 Relation and Functions
Last updated at April 16, 2024 by Teachoo
Whether binary commutative/associative or not
Chapter 1 Class 12 Relation and Functions
Concept wise
- Relations - Definition
- Empty and Universal Relation
- To prove relation reflexive, transitive, symmetric and equivalent
- Finding number of relations
- Function - Definition
- To prove one-one & onto (injective, surjective, bijective)
- Composite functions
- Composite functions and one-one onto
- Finding Inverse
- Inverse of function: Proof questions
- Binary Operations - Definition
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Whether binary commutative/associative or not
- Binary operations: Identity element
- Binary operations: Inverse
Transcript
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
