You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Equivalence Relation

In order that...

Question

In order that a relation $R$ defined on a non-empty set $A$ is an equivalence relation.
It is sufficient, if $R$

is reflexive

No worries! We‘ve got your back. Try BYJU‘S free classes today!

is symmetric

No worries! We‘ve got your back. Try BYJU‘S free classes today!

is transitive

No worries! We‘ve got your back. Try BYJU‘S free classes today!

possesses all the above three properties.

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D possesses all the above three properties.
An equivalent relation needs to be symmetric,transitive and reflexive.

Suggest Corrections

Similar questions

Q. In order that a relation R defined on a non-empty set A is an equivalence relation, it is sufficient, if R .......................

Q. In order that a relation

R

defined in a non-empty set

A

is an equivalence relation, it is sufficient that

R

Given a non-empty set X. Consider P(X), which is the set of all subset of X. Defined the relation R in P(X) as follows:
For subsets A and B in P(X),ARB if and only if $A \subset B$ . Is R an equivalence relation on P(X)? Justify your answer.

Q. Assertion :The relation

R = A \times A

( where

A

is non empty set) is an equivalence relation. Reason: Relation

R = A \times A

satisfies the property reflexivety , symmetricity and transitivity.

Q. Give a non-empty set

X

. Consider

P (X)

, which is the set of all subsets of

X

. Define the relation

R

P (X)

as follows:
For subsets

A

and

B

P (X)

A R B

A \subset B

, is

R

an equivalence relation on

P (X)

?
Justify your answer.

Join BYJU'S Learning Program

In order that a relation R defined on a non-empty set A is an equivalence relation.It is sufficient, if R

The correct option is D possesses all the above three properties.An equivalent relation needs to be symmetric,transitive and reflexive.

In order that a relation $R$ defined on a non-empty set $A$ is an equivalence relation.
It is sufficient, if $R$

The correct option is D possesses all the above three properties.
An equivalent relation needs to be symmetric,transitive and reflexive.