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Sets and Relations question

2011 · Shift 0 · Q51

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PYQ Library
JEE Main
Mathematics
Sets and Relations
2011 · Shift 0 · Q51

Sets and Relations question

2011 · Shift 0 · Q51

JEE MainMathematicsSets and RelationsMCQ+4 / −1

Let

R

be the set of real numbers. Statement I :

A=\{(x, y) \in R \times R: y-x

is an integer

\}

is an equivalence relation on

R

. Statement II :

B=\{(x, y) \in R \times R: x=\alpha y

for some rational number

\alpha\}

is an equivalence relation on

R

.

A
Statement I is true, Statement II is true; Statement II is not a correct explanation for Statement I.
B
Statement I is true, Statement II is false.
C
Statement I is false, Statement II is true.
D
Statement I is true, Statement II is true; Statement II is a correct explanation for Statement I.

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