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Example 29 - Show that addition, subtraction, multiplication - Examples

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  1. Chapter 1 Class 12 Relation and Functions
  2. Serial order wise
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Example 29 Show that addition, subtraction and multiplication are binary operations on R, but division is not a binary operation on R. Further, show that division is a binary operation on the set R∗ of nonzero real numbers. Addition + : R × R →R where (a, b) → a + b For every real number a & b, a + b is also a real number. Hence, + is a binary operation on R Subtraction – : R × R →R where (a, b) → a – b For every real number a & b, a – b is also a real number. Hence, – is a binary operation on R Multiplication × : R × R →R where (a, b) → a × b For every real number a & b, a × b is also a real number. Hence, × is a binary operation on R Division ÷ : R × R → R where (a, b) → a ÷ b Here, a & b are real numbers a ÷ b = 𝑎﷮𝑏﷯ Let a = 2 & b = 0 𝑎﷮𝑏﷯ = 𝟐﷮𝟎﷯ = Not defined Hence, ÷ is not a binary operation on R Further, show that division is a binary operation on the set R∗ of nonzero real numbers. ÷ : R* × R * →R * where (a, b) → a ÷ b For every non-zero real number a & b, a ÷ b is also a non-zero real number. Hence, ÷ is a binary operation on R*

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