Let $R _{1}$ and $R _{2}$ be two relations defined as follows :
$R _{1}=\left\{( a , b ) \in R ^{2}: a ^{2}+ b ^{2} \in Q \right\}$ and $R _{2}=\left\{( a , b ) \in R ^{2}: a ^{2}+ b ^{2} \notin Q \right\}$
where $Q$ is the set of all rational numbers. Then
Let $R _{1}$ and $R _{2}$ be two relations defined as follows :
$R _{1}=\left\{( a , b ) \in R ^{2}: a ^{2}+ b ^{2} \in Q \right\}$ and $R _{2}=\left\{( a , b ) \in R ^{2}: a ^{2}+ b ^{2} \notin Q \right\}$
where $Q$ is the set of all rational numbers. Then
- [JEE MAIN 2020]
- A
$R _{2}$ is transitive but $R _{1}$ is not transitive
- B
$R _{1}$ is transitive but $R _{2}$ is not transitive
- C
$R _{1}$ and $R _{2}$ are both transitive
- D
Neither $R _{1}$ nor $R _{2}$ is transitive
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