Let R₁ and R₂ be two relation defined as follows: R₁ = (a, b) R²: a² + b² Q and R₂ = (a, b) R²: a² + b² Q, where Q is the set of all rational numbers. Then:

(A) Neither R₁ nor R₂ is transitive.

(B) R₂ is transitive but R₁ is not transitive.

(C) R₁ and R₂ are both transitive.

(D) R₁ is transitive but R₂ is not transitive.

Sets, Relations and Functions: JEE Main 2020 Mathematics question

JEE Main 2020 · 3 Sep, Evening shift · Q5375

JEE Main 20203 Sep, Evening shiftMathematicsMediumSets, Relations and Functions168× since 2002

Let R₁ and R₂ be two relation defined as follows : R₁ = {(a, b)

\in

R² : a² + b²

\in

Q} and R₂ = {(a, b)

\in

R² : a² + b²

\notin

Q}, where Q is the set of all rational numbers. Then :

JEE Main 2020 · 3 Sep, Evening shift · Q5375

JEE Main 20203 Sep, Evening shiftMathematicsMediumSets, Relations and Functions168× since 2002

Let R₁ and R₂ be two relation defined as follows : R₁ = {(a, b)

\in

R² : a² + b²

\in

Q} and R₂ = {(a, b)

\in

R² : a² + b²

\notin

Q}, where Q is the set of all rational numbers. Then :