web analytics

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

Slide81.JPG
Slide82.JPG Slide83.JPG

  1. Chapter 1 Class 12 Relation and Functions
  2. Serial order wise
Ask Download

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 = 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*

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
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.
Jail