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Sets and Relations question

2023 · 1 Feb · Shift 2 · Q25

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PYQ Library
JEE Main
Mathematics
Sets and Relations
2023 · 1 Feb · Shift 2 · Q25

Sets and Relations question

2023 · 1 Feb · Shift 2 · Q25

JEE MainMathematicsSets and RelationsMCQ+4 / −1

Let

P(S)

denote the power set of

S=\{1,2,3, \ldots ., 10\}

. Define the relations

R_{1}

and

R_{2}

on

P(S)

as

\mathrm{AR}_{1} \mathrm{~B}

if

\left(\mathrm{A} \cap \mathrm{B}^{\mathrm{c}}\right) \cup\left(\mathrm{B} \cap \mathrm{A}^{\mathrm{c}}\right)=\emptyset

and

\mathrm{AR}_{2} \mathrm{~B}

if

\mathrm{A} \cup \mathrm{B}^{\mathrm{c}}=\mathrm{B} \cup \mathrm{A}^{\mathrm{c}}, \forall \mathrm{A}, \mathrm{B} \in \mathrm{P}(\mathrm{S})

. Then :

A
only $R_{2}$ is an equivalence relation
B
both $R_{1}$ and $R_{2}$ are not equivalence relations
C
both $R_{1}$ and $R_{2}$ are equivalence relations
D
only $R_{1}$ is an equivalence relation

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