# Example 49 - Chapter 1 Class 12 Relation and Functions (Term 1)

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Example 49 Show that the number of binary operations on {1, 2} having 1 as identity and having 2 as the inverse of 2 is exactly one. Given that 1 is identity e is the identity of * if a * e = e * a = a So, a * 1 = 1 * a = a Put a = 1 1 * 1 = 1 Put a = 2 1 * 2 = 2 * 1 = 1 Also, Given that 2 is inverse of 2 b is the inverse of a if a * b = b * a = e Here, e = 1 & a = 2, b = 2 So, 2 * 2 = 2 * 2 = 1 Hence, there is only 1 binary operation which satisfies the given conditions

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Chapter 1 Class 12 Relation and Functions (Term 1)

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About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.