# Example 29

Last updated at Dec. 8, 2016 by Teachoo

Last updated at Dec. 8, 2016 by Teachoo

Transcript

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 = 𝑎𝑏 Let a = 2 & b = 0 𝑎𝑏 = 𝟐𝟎 = 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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Example 29 You are here

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Chapter 1 Class 12 Relation and Functions

Serial order wise

About the Author

CA Maninder Singh

CA Maninder Singh is a Chartered Accountant for the past 8 years. He provides courses for Practical Accounts, Taxation and Efiling at teachoo.com .