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Transitive Relations

Let A= 1, 2, ...

Question

Let A={ 1, 2, 3, 4} and R= {( 2, 2), (3, 3), (4, 4), (1, 2)} be a relation on A. Then R is

A

Reflexive

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B

Symmetric

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C

Transitive

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D

None of these

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Solution

The correct option is B Transitive
$\neq$ R as every element is not related to itself.
$\neq$ S as (1, 2) $\in$ R but (2, 1) $\notin$ R
T (1,2), $\in$ R, (2, 2) $\in$ R
$\Rightarrow$ (1, 2)o (2, 2) = (1, 2) $\in$ R

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Similar questions

R = {(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)}

be a relation on the set

A = {1, 2, 3, 4}

R

A = {1, 2, 3, 4}

R

be a relation in

A

R = {(1, 1), (2, 2), (3, 3), (4, 4), (1, 2), (2, 1), (3, 1), (1, 3)}

then identify the relation

R

.

A = {1, 2, 3, 4}

R

be a relation in

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R = {(1, 1), (2, 2), (3, 3), (4, 4), (1, 2), (3, 1), (1, 3)}

R

Q. Let A = {1, 2, 3, 4} and R be a relation in A given by R = {(1, 1), (2, 2), (3, 3), (4, 4), (1, 2), (2, 1), (3, 1), (1, 3)}. Then R is

A = {1, 2, 3, 4}

R = {(2, 2) (3, 3) (4, 4) (1, 2)}

be a relation on

A

. Then what is the nature of

^{'} R^{'}

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