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Sets and Relations question

2024 · 1 Feb · Shift 2 · Q34

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PYQ Library
JEE Main
Mathematics
Sets and Relations
2024 · 1 Feb · Shift 2 · Q34

Sets and Relations question

2024 · 1 Feb · Shift 2 · Q34

JEE MainMathematicsSets and RelationsMCQ+4 / −1

Consider the relations

R_1

and

R_2

defined as

a R_1 b \Leftrightarrow a^2+b^2=1

for all

a, b \in \mathbf{R}

and

(a, b) R_2(c, d) \Leftrightarrow a+d=b+c

for all

(a, b),(c, d) \in \mathbf{N} \times \mathbf{N}

. Then :

A
$R_1$ and $R_2$ both are equivalence relations
B
Only $R_1$ is an equivalence relation
C
Only $R_2$ is an equivalence relation
D
Neither $R_1$ nor $R_2$ is an equivalence relation

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