Let a set $A=A_1 \cup A_2 \cup \ldots \cup A_k$. where $A_i \cap A_j=\phi$ for $i \neq j, 1 \leq i, j \leq k$. Define the relation $R$ from $A$ to $A$ by $R=\left\{(x, y): y \in A_i\right.$ if and only if $x \in A_i, 1 \leq i \leq$ $k\}$. Then, $R$ is :

Reflexive, symmetric but not transitive

Reflexive, transitive but not symmetric

Reflexive but not symmetric and transitive

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JEE MATHEMATICS MCQ: RELATIONS

1 Easy

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Analyzing +4 | -1

Let a set

A=A_1 \cup A_2 \cup \ldots \cup A_k

. where

A_i \cap A_j=\phi

for

i \neq j, 1 \leq i, j \leq k

. Define the relation

R

from

A

A

R=\left\{(x, y): y \in A_i\right.

if and only if

x \in A_i, 1 \leq i \leq

k\}

. Then,

R

is :

View answer and explanation

Correct option: D

An equivalence relation

The correct answer is D (An equivalence relation) because the relation R is reflexive, symmetric, and transitive, satisfying the definition of an equivalence relation.

JEE MATHEMATICS MCQ: RELATIONS

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