First slide

Introduction to Relations (XI) on Sets

Question

Total number of equivalence relations defined in the set _{$S = {a, b, c}$} is:

Easy

A

5
B

3!
C

_$2^{3}$
D

_$3^{3}$

Solution

The smallest equivalence relation is the identify relation
_{$R_{1} = {(a, a), (b, b) (c, c)}$}

Then two ordered pairs of two distinct elements can be added to give three more equivalence relations _{$R_{2} = {(a, a), (b, b) (c, c) (a, b), (b, a)}$}

Similarly _{$R_{3}$} and _{$R_{4}$} .finally the largest equivalence relation i.e., the universal relation

_{$R_{5} = {(a, a), (b, b) (c, c) (a, b), (b, a), (a, c), (c, a) (b, c) (c, b)}$}

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