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Let T be the set of all triangles in a ...

Let T be the set of all triangles in a plane with R a relation in T given by` R ={(T _(1) , T _(2)): T _(1)` is congruent to `T _(2)`} Show that R is an equivalence relation.

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Let L be the set of all lines in XY plane and R be the relation in L defined as R = {(L _(1) , L _(2)) : L _(1) is parallel to L _(2)}. Show that R is an equivalence relation. Find the set of all lines related to the line y = 2x +4.

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Knowledge Check

  • Let T be set of all triangle in the Euclidean plane , and let a relation R on T be defined as aRb if a is congruent to b,AA "a",b inT . Then, R is ....

    A
    Reflexive but not transitive
    B
    Transitive but not symmetric
    C
    Equivalence
    D
    None of these

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