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),

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1.Relation and Function

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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

Reflexive

B

Transitive

C

An equivalence relation

D

none of these

Solution

(a) $(1, 1)(2, 2)(3, 3)(4, 4) \in R$

$\therefore$ $R$ is reflexive.

$\therefore $ $(1, 2) (3, 1)$$ \in R$ and also $(2, 1)(1, 3) $$ \in R$

Hence, $R$ is symmetric. But clearly $R$ is not transitive.

Standard 12

Mathematics

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