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Arithmetic Aptitude :: Sets, Relations and Functions

  1.  If A Í B, then B’ – A’ is equal to

  2. A.

    ?

    B.

    A'

    C.

    B'

    D.

    A-B


  3.  If for a ? N, aN = {ax: x ? N}, then the set 6 N ? 8 N is equal to

  4. A.

    8N

    B.

    48N

    C.

    24N

    D.

    72N


  5.  Let R be a relation N define by x + 2y = 8 . The domain of R is

  6. A.

    {2,4,6}

    B.

    {2,4,8}

    C.

    {1,2,3,4}

    D.

    {2,4,6,8}


  7.  If X = {1, 2, 3, 4, 5, 6, 7, 8, 9} A = {x ? N: 30 < x2 < 70}, B = {x : x is a prime number less than 10}, then which of the following is false:

  8. A.

    A-B = {6, 8}

    B.

    A? B = {7, 8}

    C.

    A ? B = {2, 3, 5, 6, 8}

    D.

    A U B = {2, 3, 5, 6, 7, 8}


  9.  If for two sets A and B, A U B = A? B = A, then we have

  10. A.

    A = B

    B.

    B ? A ?

    C.

    A- B ? f

    D.

    None of these


  11.  The set (A U B U C) ? (A ? B’ ? C’)’ ? C’ is equal to

  12. A.

    B?C'

    B.

    A ? C

    C.

    B' ? C'

    D.

    none of these.


  13.  A survey shows that 63% of the Americans like cheese whereas 76% like apples. If x% of the Americans like both cheese and apples, then we have

  14. A.

    x ? 39

    B.

    x ? 63

    C.

    39 ? x ? 63

    D.

    none of these


  15.  If aN = {an : n ? N} and bN ? cN = dN, where a, b, c ? N and b, c are coprime, then

  16. A.

    a = bd

    B.

    b = cd

    C.

    c = bd

    D.

    d = bc


  17.  If A = {1, 2, 3, 6, 11,18, 21}, B = {5, 7, 9} and N is the universal set, then A’ U ((AU B) ? B’) is equal to

  18. A.

    A

    B.

    B

    C.

    N

    D.

    N-A


  19.  Which of the following is not correct?

  20. A.

    A ÍA' if and only if A = ?

    B.

    B = C if and only if A U B = A U C and A ? B = A? C

    C.

    A' Í A if and only if A = X, where X is the universal set

    D.

    All of these