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Sets and Relations question

2010 · Shift 0 · Q50

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PYQ Library
JEE Main
Mathematics
Sets and Relations
2010 · Shift 0 · Q50

Sets and Relations question

2010 · Shift 0 · Q50

JEE MainMathematicsSets and RelationsMCQ+4 / −1

Consider the following relations

R=\{(x, y) \mid x, y

are real numbers and

x=w y

for some rational number

w\}

;

S=\left\{\left(\frac{m}{n}, \frac{p}{q}\right) \mid m, n, p\right.

and

q

are integers such that

n, q eq 0

and

q m=p m\}

. Then

A
$R$ is an equivalence relation but $S$ is not an equivalence relation
B
Neither $R$ nor $S$ is an equivalence relation
C
$S$ is an equivalence relation but $R$ is not an equivalence relation
D
$R$ and $S$ both are equivalence relations

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