**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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About the Author

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.