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Standard IX

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

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is symmetric

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is transitive

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possesses all the three properties

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Solution

The correct option is D possesses all the three properties
For R to be an equivalence relation it should satify all 3 properties i.e. reflexive, symmetric & transitive

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Similar questions

Q. In order that a relation

R

defined in a non-empty set

A

is an equivalence relation, it is sufficient that

R

Q. In order that a relation

R

defined on a non-empty set

A

is an equivalence relation.
It is sufficient, if

R

How many of the following statements are wrong

1. A relation is said to be reflexive on set A if each element in A is related to itself.

2. Empty relation defined on a non- empty set is reflexive

3. We can define a reflexive relation on A x B, where A is not a subset of B.

4. In a reflexive relation, all the elements should be of the form (a,a) for all a from the set on which the relation is defined

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.

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 on a non-empty set A is an equivalence relation, it is sufficient, if R .......................

The correct option is D possesses all the three propertiesFor R to be an equivalence relation it should satify all 3 properties i.e. reflexive, symmetric & transitive

The correct option is D possesses all the three properties
For R to be an equivalence relation it should satify all 3 properties i.e. reflexive, symmetric & transitive