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If R be a relation lt from A ={ 1,2,3,4...

If R be a relation `lt` from A ={ 1,2,3,4 } to B = { 1,3,5} i.e (a,b ) `in` R iff a `lt` b then `R^(-1)` is { (3,1), (k,1), (3,2), (k,2), (k,3), (k,4) } what will be the value of k ?

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Knowledge Check

  • Let A = {1,2,3,4} and R be a relation in A given by R = {(1,1) (2,2) (3,3) (4,4) (1,2) (2,1) (3,1) (1,3)} . Then R is

    A
    reflexive
    B
    symmetric
    C
    transitive
    D
    an equivalence relation

  • Points (2k, 3k), (1, 0), (0, 1) and (0, 0) will be concyclic if the value of k is equal to-

    A
    k=0
    B
    k=1
    C
    `k = (5)/(13)`
    D
    k=5

  • Let R be 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)}. Choose the correct answer.

    A
    R is reflexive 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

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    When is a relation R on a set A not antisymmetric? Let A={1,2,3,4} and R be a relation on A defined by R={(1,1), (2,2), (3,4), (3,3),(2,1), (4,3)}. Is R antisymmetric on A?

    When is a relation R on a set A not transitive ? Let A={1,2,3,4} and a relation R on A be given by R={(2,3),(2,2), (3,1), (3,2), (4,1)} Is R transitive on A?

    Show that the relation R on the set A={1,2,3,4,5} given by R={(a,b):|a-b| is even} is an equivalence relation.

    Prove that the relation R in set A = {1, 2, 3, 4, 5} given by R = {(a,b): |a-b| is even} is an equivalence relation .

    The value of tan ^(-1) (1) + cos ^(-1) (-(1)/(2) ) + sin ^(-1) (-(1)/(2)) is equal to (3pi)/(k) . Find the value of K.

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