Let R be the real line. Consider the following subsets of the plane $R \times R$ : $S = \left\{ {(x,y):y = x + 1\,\,and\,\,0 < x < 2} \right\}$ $T = \left\{ {(x,y): x - y\,\,\,is\,\,an\,\,{\mathop{\rm int}} eger\,} \right\}$, Which one of the following is true ?

Question

Let R be the real line. Consider the following subsets of the plane $R \times R$ :
$S = \left\{ {(x,y):y = x + 1\,\,and\,\,0 < x < 2} \right\}$
$T = \left\{ {(x,y): x - y\,\,\,is\,\,an\,\,{\mathop{\rm int}} eger\,} \right\}$,

Which one of the following is true ?

Neither S nor T is an equivalence relation on R

Both S and T are equivalence relation on R

S is an equivalence relation on R but T is not

T is an equivalence relation on R but S is not

Solution

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