Let R1 and R2 be two relations defined as follows : 22 2 1R ab a b Q = Î +Î {( , ) : } R and 22 2 2 R ab a b Q = Î +Ï {( , ) : } R , where Q is the set of all rational numbers. Then :

Question:
Let $R_{1}$ and $R_{2}$ be two relations defined as follows :
$R_{1}=\left\{(a, b) \in \mathbf{R}^{2}: a^{2}+b^{2} \in Q\right\}$ and
$R_{2}=\left\{(a, b) \in \mathbf{R}^{2}: a^{2}+b^{2} \notin Q\right\}$, where $Q$ is the set of all rational numbers. Then :

Neither $R_{1}$ nor $R_{2}$ is transitive.
$R_{2}$ is transitive but $R_{1}$ is not transitive.
$R_{1}$ is transitive but $R_{2}$ is not transitive.
$R_{1}$ and $R_{2}$ are both transitive.

Correct Option: 1

JEE Main Previous Year 1 Question of JEE Main from Mathematics Sets, Relations and Functions chapter.

JEE Main Previous Year Sep. 03, 2020 (II)

Solution:

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