JEE Main 2020 (Online) 3rd September Evening Slot | Sets and Relations Question 85 | Mathematics

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 :

Neither R₁ nor R₂ is transitive.

R₂ is transitive but R₁ is not transitive.

R₁ and R₂ are both transitive.

R₁ is transitive but R₂ is not transitive.

JEE Main 2020 (Online) 3rd September Morning Slot

MCQ (Single Correct Answer)

-1

Consider the two sets :
A = {m $$ \in $$ R : both the roots of
x² – (m + 1)x + m + 4 = 0 are real}
and B = [–3, 5).
Which of the following is not true?

A $$ \cap $$ B = {–3}

B – A = (–3, 5)

A $$ \cup $$ B = R

A - B = ($$ - $$$$ \propto $$, $$ - $$3) $$ \cup $$ (5, $$ \propto $$)

JEE Main 2020 (Online) 2nd September Morning Slot

MCQ (Single Correct Answer)

-1

If R = {(x, y) : x, y $$ \in $$ Z, x² + 3y² $$ \le $$ 8} is a relation on the set of integers Z, then the domain of R^–1 is :

{0, 1}

{–2, –1, 1, 2}

{–1, 0, 1}

{–2, –1, 0, 1, 2}