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Question 24 (a) - 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 24 (a) Determine which of the following binary operations on the set R are associative and which are commutative. (a) a * b = 1 ∀ a, b ∈ R Check commutative * is commutative if a * b = b * a Since a * b = b * a ∀ a, b ∈ R * is commutative a * b = 1 Check associative * is associative if a (a * b) * c = a * (b * c) Since (a * b) * c = a * (b * c) ∀ a, b, c ∈ R * is an associative binary operation Check associative * is associative if a (a * b) * c = a * (b * c) Since (a * b) * c = a * (b * c) ∀ a, b, c ∈ R * is an associative binary operation a * (b * c) = a * 1 = 1
