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JEE Main & Advanced Sample Paper JEE Main Sample Paper-30

  • question_answer
    Let R be the real line. Consider the following subsets of the plane\[R\times R\]. \[S=\{(x,y):x-y+1=0\]and \[0<x<2\}\] \[T=\{(x,y):x-y\]is an integer} Which one of the following is true?

    A)  Both S and T are equivalence relations on R.

    B)  S is an equivalence relation on R but T is not.

    C)    T is an equivalence relation R but S is not.

    D)  Neither S nor T is an equivalence relation on R.

    Correct Answer: C

    Solution :

    \[T=\{(x,y):x-y\in I\}\]as \[0\in I,\] T is a reflexive relation. If \[x-y\in I\Rightarrow y-x\in I\] \[\therefore \]T is symmetrical also.                              If \[x-y={{I}_{1}},\] and \[y-z={{I}_{2}}\] Then \[x-z=x-y+y-z\] and \[{{I}_{2}}+{{I}_{2}}\in I\] \[\therefore \]T is also transitive.


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