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The minimum number of elements that must...

The minimum number of elements that must be added to the relation `R = { (1,2), (2,3)}` on the set of natural numbers so that it is an equivalence is

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The correct Answer is:
`7`
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The maximum number of equivalence relations can be defined on the set A={1,2,3} are

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Knowledge Check

  • Let R be a relation defined by R={(1,3),(2,4),(5,1)} on the set of natural number N. Then R^(-1) is equal to

    A
    `{(3,1),(4,2),(1,5)}`
    B
    `{(5,1),(4,2),(1,3)}`
    C
    `{(5,1),(2,4),(1,3)}`
    D
    None of these

  • The relation R is defined on the set of natural numbers as {(a,b): a = 2b}, the R^(-1) is given by

    A
    `{(2,1)(4,2)(6,3),...}`
    B
    `{(1,2)(2,4)(3,6),...}`
    C
    `R^(-1)` is not defined
    D
    None of these

  • The number of elements of the set {x: X in N,x^(2) = 1} where N is the set of all natural numbers is :

    A
    2
    B
    1
    C
    0
    D
    3

    • Similar Questions

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    R={(1,2),(2,3),(3,4)} be a relation on the set of natural numbers. Then the least number of elements that must be included in R to get a new relation S where S is an equivalence relation is

    The relation R={(1,3),(3,5)} is defined on the set with minimum number of elements of natural numbers. The minimum number of elements to be included in R so that R is an equivalence relation, is

    Given the relation R={(1,2),(2,3)} on the set {1,2,3) , the minimum number of ordered pairs which when added to R make it an equivalence relation is

    Let the relation R in the set of natural numbers be defined as b le a ^(2). Then, the equivalence class containing 2 is :

    The maximum number of equivalence relations on the set A = {1,2,3,4} are

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