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Sets and Relations question

2008 · Shift 0 · Q53

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PYQ Library
JEE Main
Mathematics
Sets and Relations
2008 · Shift 0 · Q53

Sets and Relations question

2008 · Shift 0 · Q53

JEE MainMathematicsSets and RelationsMCQ+4 / −1

Let R be the real line. Consider the following subsets of the plane

R \times R

:

S = \left\{ {(x,y):y = x + 1\,\,and\,\,0 \lt x \lt 2} \right\}T = \left\{ {(x,y): x - y\,\,\,is\,\,an\,\,{\mathop{\rm int}} eger\,} \right\}

, Which one of the following is true ?

A
Neither S nor T is an equivalence relation on R
B
Both S and T are equivalence relation on R
C
S is an equivalence relation on R but T is not
D
T is an equivalence relation on R but S is not

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