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

(D) T is an equivalence relation on R but S is not

(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

Sets, Relations and Functions: JEE Main 2008 Mathematics question

JEE Main 2008 · Annual, Paper 1 · Q5370

JEE Main 2008Annual, Paper 1MathematicsMediumSets, Relations and Functions168× since 2002

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 ?

JEE Main 2008 · Annual, Paper 1 · Q5370

JEE Main 2008Annual, Paper 1MathematicsMediumSets, Relations and Functions168× since 2002

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 ?