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Arithmetic Aptitude :: Sets, Relations and Functions

Sets, Relations and Functions - Section-1
  1.  Which of the following sets are null sets ?

    2. A.

    { }
    B.

    ø
    C.

    Both (a) and (b)
    D.

    {0}

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  2.  Let R be a non-empty relation on a collection of sets defined by ARB if and only if A ∩ B = Ø Then (pick the TRUE statement)

    3. A.

    R is relexive and transitive
    B.

    R is an equivalence relation
    C.

    R is symmetric and not transitive
    D.

    R is not relexive and not symmetric

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  3.  The binary relation S = Φ (empty set) on set A = {1, 2,3} is

    4. A.

    transitive and relexive
    B.

    symmetric and relexive
    C.

    transitive and symmetric
    D.

    neither reflexive nor symmetric

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  4.  Number of subsets of a set of order three is

    5. A.

    2
    B.

    4
    C.

    6
    D.

    8

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  5.  "n/m" means that n is a factor of m, then the relation T is

    6. A.

    relexive, transitive and not symmetric
    B.

    relexive, transitive and symmetric
    C.

    transitive and symmetric
    D.

    relexive and symmetric

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  6.  If R be a symmetric and transitvie relation on a set A, then

    7. A.

    R is not reflexive and hence not an equivalence relation
    B.

    R is reflexive and hence an equivalence relation
    C.

    R is reflexive and hence a partial order
    D.

    None of these

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  7.  Let P(S) denote the power set of set S. Which of the following is always TRUE ?

    8. A.

    S ∉ P(S)
    B.

    P(P(S)) = P(S)
    C.

    P(S)  ∩ S = P (S)
    D.

    P(S)  ∩ P(P(S))  = [ φ ]

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  8.  The number of elements in the Power set P(S) of the set S = [ [ Φ] , 1, [ 2, 3 ]] is

    9. A.

    2
    B.

    4
    C.

    6
    D.

    8

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  9.  If A and B are sets and A∪ B= A ∩ B, then

    10. A.

    A = B
    B.

    A = Φ
    C.

    B = Φ
    D.

    none of these

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  10.  Let S be an infinite set and S1, S2, S3, ..., Sn be sets such that S1 ∪S2 ∪S3∪ .......Sn = S then

    11. A.

    atleast one of the sets Si is a finite set
    B.

    atleast one of the sets Si is an ininite set
    C.

    not more than one of the set Si can be inite
    D.

    none of these

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