Let a set A=A_{1} cup A_{2} cup ldots cup A_{k,} quad where A_{ i } cap A _{ j }=phi for i ≠ j 1 ?

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1.Relation and Function

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Let a set $A=A_{1} \cup A_{2} \cup \ldots \cup A_{k,} \quad$ 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 $\left.x \in A_{i}, 1 \leq i \leq k\right\}$. Then, $R$ is

A

reflexive, symmetric but not transitive

B

reflexive, transitive but not symmetric

C

reflexive but not symmetric and transitive

D

an equivalence relation

(JEE MAIN-2022)

Solution

$A =\{1,2,3\}$

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

Standard 12

Mathematics

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