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Transitive Relations

The relation ...

Question

The relation $R = {(1, 1), (2, 2), (3, 3)}$ on the set ${1, 2, 3}$ is

A

Reflexive relation only

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B

Reflexive and Symmetric relation only

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C

Equivalence relation

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D

Reflexive but not Transitive relation

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Solution

The correct option is C Equivalence relation
$R$ is an identity relation on the set ${1, 2, 3}$ and we know that an identity relation is always an equivalence relation.

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R

is an equivalence relation on a set

A

R^{- 1}

Q. The relation R = {(1, 1), (2, 2), (3, 3)} on the set {1, 2, 3} is
(a) symmetric only
(b) reflexive only
(c) an equivalence relation
(d) transitive only

R = {(3, 3), (6, 6), (9, 9), (12, 12), (6, 12), (3, 9), (3, 12), (3, 6)}

be a relation on the set

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. The relation is

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A

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

R \cup S

Q. The relation

R

R

R = {(a, b) : a \leq b},

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Transitive Relations

Standard XII Mathematics

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