Question 25 - Binary operations: Inverse - Chapter 1 Class 12 Relation and Functions
Last updated at April 16, 2024 by Teachoo
Binary operations: Inverse
Question 22 Deleted for CBSE Board 2024 Exams
Question 23 Deleted for CBSE Board 2024 Exams
Question 25 Deleted for CBSE Board 2024 Exams You are here
Question 10 Important Deleted for CBSE Board 2024 Exams
Question 6 Important Deleted for CBSE Board 2024 Exams
Question 9 Important Deleted for CBSE Board 2024 Exams
Binary operations: Inverse
Last updated at April 16, 2024 by Teachoo
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