Subscribe to our Youtube Channel - https://www.youtube.com/channel/UCZBx269Tl5Os5NHlSbVX4Kg

Last updated at Jan. 28, 2020 by Teachoo

Transcript

Example 44 Let f : X → Y be a function. Define a relation R in X given by R = {(a, b): f(a) = f(b)}. Examine whether R is an equivalence relation or not. Equivalence relation are Relations which are reflexive, transitive and symmetric. R = {(a, b): f(a) = f(b)} Check reflexive Since f (a) = f (a), ∴ (a, a) ∈ R, Hence, R is reflexive. Check symmetric If f (a) = f (b), then f (b) = f (a) Hence, (b, a) ∈ R So, if (a, b) ∈ R , then (b, a) ∈ R. ∴ R is symmetric. Check transitive If (a, b) ∈ R ∴ f(a) = f(b) Also if, (b, c) ∈ R ∴ f(b) = f(c) From (1) & (2) f(a) = f(c) ∴ (a, c) ∈ R, ∴ If (a, b) ∈ R & (b, c) ∈ R , then (a, c) ∈ R ∴ R is transitive. Hence, R is an equivalence relation.

Examples

Example 1

Example 2

Example 3

Example 4 Important

Example 5

Example 6 Important

Example 7

Example 8

Example 9

Example 10

Example 11 Important

Example 12 Important

Example 13 Important

Example 14 Important

Example 15

Example 16

Example 17

Example 18 Important

Example 19 Important

Example 20

Example 21

Example 22

Example 23 Important

Example 24

Example 25 Important

Example 26

Example 27 Important

Example 28

Example 29

Example 30

Example 31

Example 32

Example 33

Example 34

Example 35

Example 36

Example 37

Example 38

Example 39

Example 40

Example 41 Important

Example 42 Important

Example 43 Important

Example 44 You are here

Example 45 Important

Example 46 Important

Example 47 Important

Example 48 Important

Example 49

Example 50

Example 51 Important

Chapter 1 Class 12 Relation and Functions

Serial order wise

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.