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Example 34 - Show that +, x are commutative binary, but - Whether binary commutative/associative or not

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Slide95.JPG

  1. Chapter 1 Class 12 Relation and Functions
  2. Serial order wise
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Example 34 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 = 𝑎﷮𝑏﷯ = 2﷮5﷯ b ÷ a = 𝑏﷮𝑎﷯ = 5﷮2﷯ Since a ÷ b ≠ b ÷ a Hence, ÷ is not a commutative 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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