Question 12 - Binary Operations - Definition - Chapter 1 Class 12 Relation and Functions

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

Example 29 - Chapter 1 Class 12 Relation and Functions - Part 2
Example 29 - Chapter 1 Class 12 Relation and Functions - Part 3
Example 29 - Chapter 1 Class 12 Relation and Functions - Part 4

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Question 12 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 = Let a = 2 & b = 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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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.