If R is the smallest equivalence relation on the set ... | Relation (Mathematics)

JEE Mains ( $29^{th\ }$ Jan $2^{nd\ }$ Shift 2024)

Mathematics

R

is the smallest equivalence relation on the set

\{ 1,2,3,4\}

such that

\{(1,2),(1,3)\} \subset R

, then the number of elements in

R

\

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Correct Answer:

Explanation

(c) : To make $R$ an equivalence relation, $\\R$ should be reflexive, symmetric and transitive $\\ \therefore R = \{(1,1),(2,2),(3,3)(4,4)(1,2),(2,1),(1,3)$ , $(3,1),(3,2),(2,3)\}\\$ So, minimum number of elements in $R$ should be 10 .

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