Let R={(1,2),(2,3),(3,3)} be a relation defined on set {1,2,3,4} . Then minimum number of elements,

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1.Relation and Function

medium

Let $R=\{(1,2),(2,3),(3,3)\}$ be a relation defined on the set $\{1,2,3,4\}$. Then the minimum number of elements, needed to be added in $R$ so the $R$ becomes an equivalence relation, is :

A$10$

B$8$

C$9$

D$7$

(JEE MAIN-2025)

Solution

$A=\{1,2,3,4\}$
For relation to be reflexive
$R=\{(1,2),(2,3),(3,3)\}$
Minimum elements added will be
$(1,1),(2,2),(4,4)(2,1)(3,2)(3,2)(3,1)(1,3)$
$\therefore$ Minimum number of elements $=7$

Standard 12

Mathematics

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(JEE MAIN-2024)

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(JEE MAIN-2025)

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medium

Let $R=\{(1,2),(2,3),(3,3)\}$ be a relation defined on the set $\{1,2,3,4\}$. Then the minimum number of elements, needed to be added in $R$ so the $R$ becomes an equivalence relation, is :

Solution

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