Question 10 - Chapter 1 Class 12 Relation and Functions (Important Question)
Last updated at April 16, 2024 by Teachoo
Chapter 1 Class 12 Relation and Functions
Ex 1.2 , 10 Important
Example 17 Important
Question 8 Important Deleted for CBSE Board 2024 Exams
Ex 1.3, 3 (i) Important Deleted for CBSE Board 2024 Exams
Ex 1.3 , 6 Deleted for CBSE Board 2024 Exams
Ex 1.3 , 8 Important Deleted for CBSE Board 2024 Exams
Ex 1.3 , 9 Important Deleted for CBSE Board 2024 Exams
Ex 1.3, 13 (MCQ) Important Deleted for CBSE Board 2024 Exams
Ex 1.3, 14 (MCQ) Important Deleted for CBSE Board 2024 Exams
Ex 1.4, 11 Important Deleted for CBSE Board 2024 Exams
Question 3 Important Deleted for CBSE Board 2024 Exams
Misc 1 Important
Question 10 Important Deleted for CBSE Board 2024 Exams You are here
Question 11 Deleted for CBSE Board 2024 Exams
Chapter 1 Class 12 Relation and Functions
Last updated at April 16, 2024 by Teachoo
Question 10 Define a binary operation *on the set {0, 1, 2, 3, 4, 5} as a * b = {█(𝑎+𝑏, 𝑖𝑓 𝑎+𝑏<6@&𝑎+𝑏 −6, 𝑖𝑓 𝑎+𝑏≥6)┤ Show that zero is the identity for this operation and each element a ≠ 0 of the set is invertible with 6 − a being the inverse of a. e is the identity of * if a * e = e * a = a Checking if zero is identity for this operation If a + b < 6 Putting b = 0 a < 6 This is possible Now, a * 0 = a + 0 = a 0 * a = 0 + a = a Thus, a * 0 = 0 * a = a So, 0 is identity of * If a + b ≥ 6 Putting b = 0 a ≥ 6 This is not possible as value of a can be {0, 1, ,2, 3, 4, 5} Now, we need to show that each element a ≠ 0 of the set is invertible with 6 − a being the inverse of a. a * b = {█(𝑎+𝑏, 𝑖𝑓 𝑎+𝑏<6@&𝑎+𝑏 −6, 𝑖𝑓 𝑎+𝑏≥6)┤ An element a in set is invertible if, there is an element in set such that , a * b = e = b * a Putting b = 6 – a So, a + b = a + (6 – a) = 6 Since a + b ≥ 6 a * b = a + b – 6 a * b = a * (6 – a) = a + (6 – a) – 6 = 0 b * a = (6 – a) * a = (6 – a) + a – 6 = 0 Since a * (6 – a) = (6 – a) * a = 0 Hence, each element a of the set is invertible with 6 − a being the inverse of a. s