Question 25 - Examples - Chapter 1 Class 12 Relation and Functions

Last updated at Dec. 16, 2024 by

Example 49 - Show number of binary operations on {1, 2} - Binary operations: Inverse

Example 49 - Chapter 1 Class 12 Relation and Functions - Part 2

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Question 25 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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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 and Computer Science at Teachoo