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Arithmetic Aptitude :: Sets, Relations and Functions

  1.  If A Í B then which of the following are correct?

  2. A.

    A- B = ?

    B.

    A U B = B

    C.

    A ? B = B - A

    D.

    All of these


  3.  If A U B = AU C and A ? B = A ? C, then

  4. A.

    B = C

    B.

    B = C only when A Í C

    C.

    B = C only when A ? B

    D.

    none of these


  5.  If A = {(x, y) : x2 + y2 = 1; x, y ? R} and B = {(x, y): x2 + y2 = 4; x, y ?R} then

  6. A.

    A ? B = ?

    B.

    A ? B ? f

    C.

    A ? B = ?

    D.

    B ?A = B


  7.  Let X be the universal set for sets A and B. If n (A) = 200, n (B) = 300 and n (A?B) = 100, then n(A’? B’) is equal to 300 provided n(X) is equal to

  8. A.

    500

    B.

    600

    C.

    700

    D.

    800


  9.  Which of the following does not have a proper subset

  10. A.

    {x: x ? Q}

    B.

    {x: x ? Q, 3 < x < 4

    C.

    {x: x ? N, 3 < x < 4}

    D.

    none of these


  11.  If A = {4n -3n -1: n ? N} and B = {9(n-1): n ? N}, then we have

  12. A.

    B Í A

    B.

    A Ì B

    C.

    A? B = ?

    D.

    none of these


  13.  Let A = {x: x is a digit in the number 3591}, B = {x: x ? N, x<10}. Which of the following is false?

  14. A.

    A? B = {1,3,5,9}

    B.

    A-B = {2,4,6,7,8}

    C.

    A U B = {1,2,3,4,5,6,7,8,9}

    D.

    none of these


  15.  Two finite sets have m and n elements. The total number of subsets of the first set is 56 more than the total number of subsets of the second set. The values of m and n are respectively

  16. A.

    4,1

    B.

    6, 3

    C.

    8, 5

    D.

    none of these


  17.  Which of the following are true:

  18. A.

    1 and 2

    B.

    {x: x >3, x ?0} ? ?

    C.

    {x: x2-1= 0, x ?N} ? {-1, 1}

    D.

    {x: x2 - 4x + 3 = 0} = {1, 3}


  19.  Which of the following sets are null sets:

  20. A.

    2 and 3

    B.

    {x: x < 5, x > 6}

    C.

    {x: |x |< -4, x ?N}

    D.

    Set of all prime numbers between 15 and 19