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Example 45 - Determine binary operations as associative - Examples

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  1. Chapter 1 Class 12 Relation and Functions
  2. Serial order wise
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Example 45 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 Check associative * 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 Example 45 Determine which of the following binary operations on the set R are associative and which are commutative. (b) a ∗ b = (a + b)﷮2﷯ ∀ a, b ∈ R Check commutative * is commutative if a * b = b * a Since a * b = b * a ∀ a, b ∈ R * is commutative Check associative * 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

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
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