First slide

Relations XII

Question

The minimum number of elements that must be added to the relation $R = {(1, 2), (2, 3)}$ on the sub set ${1, 2, 3}$ of natural numbers so that it is an equivalence relation is

Moderate

A

4
B

7
C

6
D

5

Solution

$R$ is reflexive if $(x, x) \in R$ for all $x \in {1, 2, 3}$
$\Rightarrow (1, 1), (2, 2), (3, 3) \in R$
$R$ is symmetric if $(1, 2), (2, 3) \in R$
$\Rightarrow (1, 3) \in R$ also $(3, 1) \in R$ as
$R$ is transitive if $(1, 2), (2, 3) \in R$
$\Rightarrow (1, 3) \in R$ also $(3, 1) \in R$ as
$R$ is symmetric.
So the total numbers of elements is $9 .$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App