Let a set A = A _ 1 A _ 2 A _ k , where A _ i A _ j = ϕ for i ≠ j; 1 ≤ i, j ≤ k . Define the relation R from A to A by R = \ (x, y): y ∈ A _ i if and only if x ∈ A _ i , 1 ≤ i ≤ k\ . Then, R is:

Correct answer: D. an equivalence relation Let A = \ 1, 2, 3\ Then R = \ (1, 1), (1, 2), (1, 3)(2, 1), (2, 2), (2, 3)(3, 1), (3, 2)(3, 3)\ which is an equivalence relation.

JEE Main 202229 JuneMorning Shift

Exam: JEE Main
Year: 2022
Date: 29 June
Shift: Morning Shift
Subject: Mathematics
Chapter: Sets and Relations

JEE Main 2022 · 29 June · Morning Shift · Mathematics · Sets and Relations

Let a set A = A _ 1 A _ 2 A _ k , where A _ i A _ j = ϕ for i ≠ j;...

Let a set

A = {A}_{1} \cup {A}_{2} \cup \ldots \cup {A}_{k}

, where

{A}_{i} \cap {A}_{j} = ϕ

for

i \ne j; 1 \le i, j \le k .

Define the relation

R

from

A

A

R = \{\left(x, y\right): y \in {A}_{i}

if and only if

x \in {A}_{i}, 1 \le i \le k\}

. Then,

R

is:

Options

Areflexive, symmetric but not transitive
Breflexive, transitive but not symmetric
Creflexive but not symmetric and transitive
Dan equivalence relation

Correct answer

D. an equivalence relation

Step-by-step solution

Let $A = \left\{1, 2, 3\right\}$

Then $R = \left\{\left(1, 1\right), \left(1, 2\right), \left(1, 3\right)\left(2, 1\right), \left(2, 2\right), \left(2, 3\right)\left(3, 1\right), \left(3, 2\right)\left(3, 3\right)\right\}$

which is an equivalence relation.

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