# Example 19 - Chapter 1 Class 12 Relation and Functions

Last updated at April 16, 2024 by Teachoo

Examples

Example 1

Example 2

Example 3

Example 4 Important

Example 5

Example 6 Important

Example 7

Example 8 Important

Example 9

Example 10

Example 11 Important

Example 12 Important

Example 13 Important

Example 14 Important

Example 15

Example 16

Example 17 Important

Example 18

Example 19 Important You are here

Example 20 Important

Example 21

Example 22 Important

Example 23 Important

Example 24 Important

Example 25

Example 26 Important

Question 1 Deleted for CBSE Board 2025 Exams

Question 2 Important Deleted for CBSE Board 2025 Exams

Question 3 Important Deleted for CBSE Board 2025 Exams

Question 4 Deleted for CBSE Board 2025 Exams

Question 5 Deleted for CBSE Board 2025 Exams

Question 6 Deleted for CBSE Board 2025 Exams

Question 7 Deleted for CBSE Board 2025 Exams

Question 8 Important Deleted for CBSE Board 2025 Exams

Question 9 Deleted for CBSE Board 2025 Exams

Question 10 Important Deleted for CBSE Board 2025 Exams

Question 11 (a) Deleted for CBSE Board 2025 Exams

Question 11 (b) Deleted for CBSE Board 2025 Exams

Question 11 (c) Deleted for CBSE Board 2025 Exams

Question 12 Deleted for CBSE Board 2025 Exams

Question 13 Deleted for CBSE Board 2025 Exams

Question 14 Important Deleted for CBSE Board 2025 Exams

Question 15 Deleted for CBSE Board 2025 Exams

Question 16 Deleted for CBSE Board 2025 Exams

Question 17 Deleted for CBSE Board 2025 Exams

Question 18 Deleted for CBSE Board 2025 Exams

Question 19 Deleted for CBSE Board 2025 Exams

Question 20 Important Deleted for CBSE Board 2025 Exams

Question 21 Deleted for CBSE Board 2025 Exams

Question 22 Deleted for CBSE Board 2025 Exams

Question 23 Deleted for CBSE Board 2025 Exams

Question 24 (a) Deleted for CBSE Board 2025 Exams

Question 24 (b) Deleted for CBSE Board 2025 Exams

Question 25 Deleted for CBSE Board 2025 Exams

Chapter 1 Class 12 Relation and Functions

Serial order wise

Last updated at April 16, 2024 by Teachoo

Example 19 Let R be a relation on the set A of ordered pairs of positive integers defined by (x, y) R (u, v) if and only if xv = yu. Show that R is an equivalence relation. If (x, y) R (u, v) , then xv = yu Check Reflexive If (x, y) R (x, y), then xy = yx Since, xy = yx Hence , R is reflexive. Check symmetric If (x, y) R (u, v) , then xv = yu Now, If (u, v) R (x, y) , then uy = vx Since, xv = yu, vx = uy ∴ uy = vx So, if (x, y) R (u, v) , then (u, v) R (x, y) So, R is symmetric. If (x, y) R (u, v) , then xv = yu If (u, v) R (a, b) , then ub = va u = 𝑣𝑎/𝑏 We need to prove that (x, y) R (a, b) , i.e. xb = ya Check transitive Putting (2) in (1) xv = yu xv = y(𝑣𝑎/𝑏) xvb = yva xb = ya Hence (x, y) R (a, b) So, if (x, y) R (u, v) & (u, v) R (a, b) , then (x, y) R (a, b) Thus R is transitive. Thus, R is an equivalence relation.