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Standard XII

Mathematics

Reflexive Relations

In order that...

Question

In order that a relation $R$ defined in a non-empty set $A$ is an equivalence relation, it is sufficient that $R$

is reflexive

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is symmetric

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is transitive

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possess all the above three properties

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Solution

The correct option is D possess all the above three properties
A relation R is said to be an equivalence relation if it is
(i)Reflexive
(ii)Symmetric
(iii)Transitive

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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 on a non-empty set

A

is an equivalence relation.
It is sufficient, if

R

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.

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.

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In order that a relation R defined in a non-empty set A is an equivalence relation, it is sufficient that R

The correct option is D possess all the above three propertiesA relation R is said to be an equivalence relation if it is (i)Reflexive(ii)Symmetric(iii)Transitive

In order that a relation $R$ defined in a non-empty set $A$ is an equivalence relation, it is sufficient that $R$

The correct option is D possess all the above three properties
A relation R is said to be an equivalence relation if it is
(i)Reflexive
(ii)Symmetric
(iii)Transitive