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Ex 1.4, 2 (i) - Chapter 1 Class 12 Relation and Functions
Last updated at August 19, 2026 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
-
Whether binary commutative/associative or not
- Binary operations: Identity element
- Binary operations: Inverse
Transcript
Ex 1.4, 2 For each binary operation * defined below, determine whether * is commutative or associative. (i) On Z, define a * b = a − b Check commutative * is commutative if a * b = b * a Since a * b ≠ b * a * is not commutative a * b = a – b b * a = b – a Check associative * is associative if (a * b) * c = a * (b * c) Since (a * b) * c ≠ a * (b * c) * is not an associative binary operation (a * b)* c = (a – b) * c = (a – b) – c = a – b – c a * (b * c) = a * (b – c) = a – (b – c) = a – b + c
