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Arithmetic Aptitude :: Sets, Relations and Functions

  1.  Some group (G, 0) is known to be abelian. Then which one of the following is TRUE for G ?

  2. A.

    g = g-1 for every g ∈ G

    B.

    g = g² for every g ∈ G

    C.

    (g o h)²= g²o h² for every g,h ∈ G

    D.

    G is of finite order

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  3.  If the binary operation * is deined on a set of ordered pairs of real numbers as (a, b) * (c, d) = (ad + bc, bd) and is associative, then (1, 2) * (3, 5) * (3, 4) equals

  4. A.

    (7,11)

    B.

    (23,11)

    C.

    (32,40)

    D.

    (74,40)

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  5.  If A = (1, 2, 3, 4). Let ~ = ((1, 2), (1, 3), (4, 2). Then ~ is

  6. A.

    reflexive

    B.

    transitive

    C.

    symmetric

    D.

    not anti-symmetric

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  7.  Which of the following statements is false ?

  8. A.

    If R is relexive, then R ∩ R-1≠ φ

    B.

    R ∩ R-1≠ φ =>R is anti-symmetric.

    C.

    If R, R' are reflexive relations in A, then R - R' is reflexive

    D.

    If R, R' are equivalence relations in a set A, then R  ∩ R' is also an equivalence relation in A.

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  9.  If R = {(1, 2),(2, 3),(3, 3)} be a relation defined on A= {1, 2, 3} then R . R( = R2) is

  10. A.

    R itself

    B.

    {(1, 2),(1, 3),(3, 3)}

    C.

    {(1, 3),(2, 3),(3, 3)}

    D.

    {(2, 1),(1, 3),(2, 3)}

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  11.  Every set is a ___________ of itself

  12. A.

    Compliment

    B.

    Proper subset

    C.

    Improper subset

    D.

    None of the above

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  13.  Empty set is a ?

  14. A.

    Infinite Set

    B.

    Invalid Set

    C.

    Finite Set

    D.

    None of the above

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  15.  A’ will contain how many elements from the original set A

  16. A.

    0

    B.

    1

    C.

    Infinite

    D.

    All elements in A

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  17.  A — B will contain elements in ?

  18. A.

    A not in B

    B.

    B not in A

    C.

    Both A and B

    D.

    Neither A nor B

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  19.  A set has n elements, then the, number of elements in its power set is ?

  20. A.

    2n

    B.

    m x n

    C.

    m + n

    D.

    m - n

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