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Show that the relation R in the set {1, ...

Show that the relation R in the set {1, 2, 3} defined as R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3)} is reflexive, but neither symmetric nor transitive.

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The correct Answer is:
the given relation is reflexive and transitive but not symmetric
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Explore conceptually related problems

Show that the relation R in the set {1, 2, 3} given by R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3)} is reflexive but neither symmetric nor transitive.

The relation R on the set A = {1, 2, 3} defined as R = {(1, 1), (1, 2), (2, 1), (3, 3)} is reflexive, symmetric and transitive.

Knowledge Check

  • If a relation R on the set {1, 2, 3} be defined by R = {(1, 2)}, then R is

    A
    reflexive
    B
    transitive
    C
    symmetric
    D
    none of these

  • If a relation R on the set {1, 2, 3} be defined by R = {(1, 2)}, then R is

    A
    reflexive
    B
    transitive
    C
    symmetric
    D
    none of these

  • Let the relation in the set {1, 2, 3, 4} given by R= {(1, 2), (2, 2), (1, 1), (4,4), (1, 3), (3, 3), (3, 2) then (a)R is reflexive and symmetric but not transitive (b)R is reflexive and transitive but not symmetric (c)R is symmetric and transitive but not reflexive (d)R is an equivalence relation

    A
    R is reflexive and symmetric but not transitive
    B
    R is reflexive and transitive but not symmetric
    C
    R is symmetric and transitive but not reflexive
    D
    R is an equivalence relation

    • Similar Questions

    Explore conceptually related problems

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    The relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)} is not symmetric.

    Show that the relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)} is symmetric but neither reflexive nor transitive.

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