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Let A={(0,1,2,3} and define a relation R...

Let `A={(0,1,2,3}` and define a relation R on A as follows:
`R={(0,0),(0,1), (0,3), (1,0),(1,1),(2,2),(3,0),(3,3)}`, Is R reflexive? Symmetive? Transitive?

Text Solution

Verified by Experts

The correct Answer is:
R is reflexive and symmetric but not transitive.
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Explore conceptually related problems

Let A={0,\ 1,\ 2,\ 3} and R be a relation on A defined as R={(0,\ 0),\ (0,\ 1),\ (0,\ 3),\ (1,\ 0),\ (1,\ 1),\ (2,\ 2),\ (3,\ 0),\ (3,\ 3)} , is R reflexive? symmetric 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

  • A relation R on A is as follows R = { (0,0),(0,1),(0,3),(1,0),(1,1),(2,2),(3,0),(3,3)} for A = {0,1,2,3} . Then R is

    A
    Reflexive but not symmetric
    B
    symmetric and transitive
    C
    Reflexive symmetric but not transitive
    D
    Eqquivalence

  • For the following relation R = {(0,0),(0,1),(1,1),(2,1),(2,2),(2,0),(1,0), (0,2),(0,1) }

    A
    domain = {0,1}
    B
    range = {0,1,2}
    C
    both correct
    D
    None of these

  • Let R be a relation defined on A={1,2,3} by : R={(1,3),(3,1),(2,2)} . R is :

    A
    Reflexive
    B
    Symmetric
    C
    Transitive
    D
    Reflexive but not Transitive

    • Similar Questions

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    Check whether the relation R={(1,1),(2,2)(3,3),(1,2),(2,3),(1,3)} is reflexive,symmetric and transitive or not.

    Let A={1,\ 2,\ 3} and consider the relation R={(1,\ 1),\ (2,\ 2),\ (3,\ 3),\ (1,\ 2),\ (2,\ 3),\ (1,\ 3)} . Then, R is (a) reflexive but not symmetric (b) reflexive but not transitive (c) symmetric and transitive (d) neither symmetric nor transitive

    Let A={1,2,3,4} and R={(1,1),(2,2),(3,3),(4,4),(1,2),(1,3),(3,2)}. show that R is reflexive and transitive but not symmetric .

    Determine whether Relation R on the set A={1,\ 2,\ 3,\ ,\ 13 ,\ 14} defined as R={(x ,\ y):3x-y=0} is reflexive, symmetric or transitive.

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