# Example 6 - Chapter 1 Class 12 Relation and Functions

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Example 6 Let R be the relation defined in the set A = {1, 2, 3, 4, 5, 6, 7} by R = {(a, b) : both a and b are either odd or even}. Show that R is an equivalence relation. Further, show that all the elements of the subset {1, 3, 5, 7} are related to each other and all the elements of the subset {2, 4, 6} are related to each other, but no element of the subset {1, 3, 5, 7} is related to any element of the subset {2, 4, 6}. R = {(a, b) : both a and b are either odd or even} Check reflexive Since, a & a are the same numbers both a and a must be either odd or even, ∴ (a, a) ∈ R, So, R is reflexive Check symmetric If both a & b are either odd or even then, both b & a are either odd or even So, if (a, b) ∈ R , then (b, a)∈ R So, R is symmetric Check transitive If both a & b are either odd or even and both b & c are either odd or even , then a, b, c are either odd or even So, both a & c are either odd or even So, if (a, b) ∈ R and (b, c) ∈ R , then (a, c) ∈ R. So, R is transitive Since R is reflexive, symmetric and transitive Hence, R is an equivalence relation. Further, show that all the elements of the subset {1, 3, 5, 7} are related to each other and all the elements of the subset {2, 4, 6} are related to each other, but no element of the subset {1, 3, 5, 7} is related to any element of the subset {2, 4, 6}. R = {(a, b) : both a and b are either odd or even} In {1, 3, 5, 7}, All elements are odd, Hence, element of {1, 3, 5, 7 } are related to each other In {2, 4, 6}, All elements are even, Hence, element of {2, 4, 6} are related to each other In {1, 3, 5, 7} & {2, 4, 6}, Elements of {1, 3, 5, 7} are odd Elements of {2, 4, 6} are even One element from {1, 3, 5, 7} is odd and one element from {2, 4, 6} is even Hence, both elements cannot be either odd or even Hence, {1, 3, 5, 7} & {2, 4, 6} are not related to each other

Examples

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6 You are here

Example 7

Example 8

Example 9

Example 10

Example 11

Example 12

Example 13

Example 14

Example 15

Example 16

Example 17

Example 18

Example 19

Example 20

Example 21

Example 22

Example 23 Important

Example 24

Example 25 Important

Example 26

Example 27

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

Example 42

Example 43

Example 44

Example 45

Example 46 Important

Example 47 Important

Example 48 Important

Example 49

Example 50

Example 51

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 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.