Tough Test On Mathematics: Quiz!

14 Questions | Total Attempts: 74

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Tough Test On Mathematics: Quiz!

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Questions and Answers
  • 1. 
    What is the cardinality of the set {a, {a}, {a, {a}}}
    • A. 

      3

    • B. 

      4

    • C. 

      Does not exist

    • D. 

      0

  • 2. 
    How many elements do the following settings have where a and b are distinct elements?  P({a, b, {a, b}})
    • A. 

      8

    • B. 

      16

    • C. 

      4

    • D. 

      32

  • 3. 
    The sets A and B if A – B = {1, 5, 7, 8},  B – A = {2, 10} and A intersection B = {3, 6, 9}
    • A. 

      A = {1, 3, 5, 6, 7, 8, 9}; B = {2, 3, 6, 9, 10}

    • B. 

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

    • C. 

      A = {3, 5, 6, 8, 9}; B = {2, 6, 9, 10}

    • D. 

      A = {1, 2, 3, 4, 5, 6, 8, 9 10}; B = {2, 3, 6, 9}

  • 4. 
    What can you say about the sets A and B if we know that A – B = A
    • A. 

      A and B are disjoint

    • B. 

      A is empty set

    • C. 

      A intersection B is non-empty

    • D. 

      A union B is equal to A intersection B

  • 5. 
    The symmetric difference of {1, 3, 5} and {1, 2, 3}
    • A. 

      {2, 5}

    • B. 

      {1, 2, 5}

    • C. 

      {1, 3, 4}

    • D. 

      {1, 3}

  • 6. 
    What can you say about the sets A and B if A symmetric difference B = A
    • A. 

      B is empty set

    • B. 

      A is empty set

    • C. 

      A = B

    • D. 

      A - B = B

  • 7. 
    Suppose the universal set is U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} express the following set with bit strings where the ith bit in the string is 1 if i is the set and 0 otherwise {2, 3, 4, 7, 8, 9}  
    • A. 

      0111001110

    • B. 

      1111001010

    • C. 

      0001110011

    • D. 

      1011000110

  • 8. 
    Let R be a binary relation on A such that (a, b) belongs to R if book ‘a’ costs more and contains fewer pages than book ‘b’.  What can you say about the relation?
    • A. 

      Not reflexive, not symmetric, anti-symmetric and transitive

    • B. 

      Reflexive, not symmetric, anti-symmetric and transitive

    • C. 

      Not reflexive, not symmetric, not anti-symmetric, not transitive

    • D. 

      Reflexive, not symmetric, not anti-symmetric and transitive

  • 9. 
    Let R be a binary relation on the set of all positive integers such that R = {(a, b)/ a – b is an odd positive integer}
    • A. 

      Not reflexive, not symmetric, anti-symmetric and transitive

    • B. 

      Not reflexive, symmetric, anti-symmetric and not transitive

    • C. 

      Reflexive, not symmetric, anti-symmetric and transitive

    • D. 

      Reflexive, symmetric, not anti-symmetric and not transitive

  • 10. 
    If R = {(a, b)/ a = b2} where a, b are positive integers, then R
    • A. 

      Neither equivalence nor partial ordering relation

    • B. 

      Reflexive and symmetric but not transitive

    • C. 

      Reflexive and anti-symmetric but not transitive

    • D. 

      Not reflexive, but anti-symmetric and transitive

  • 11. 
    Let R on the set of all strings 0’s and 1’s such that R = {(a, b)/ a and b are strings that have same number of 0’s}
    • A. 

      R is an equivalence but not anti-symmetric

    • B. 

      R is a partial ordering relation but not symmetric

    • C. 

      R is both equivalence and partial ordering relation

    • D. 

      R is neither equivalence nor partial ordering relaiton

  • 12. 
    If |A union B| = 12, A is subset of B and |A| = 3, then |B| is
    • A. 

      12

    • B. 

      9

    • C. 

      Less than or equal to 9

    • D. 

      None

  • 13. 
    {[(A union B) intersection A] union B} intersection A is
    • A. 

      A

    • B. 

      B

    • C. 

      A union B

    • D. 

      A intersection B

  • 14. 
    A relation S is defined as aSb if a2 + b2 = 4, find domain of S and range of S, where S is a relation from Z to Z.
    • A. 

      D(S) = R(S) = {0, 2, -2}

    • B. 

      D(S) = {2}; R(S) = {0}

    • C. 

      D(S) = R(S) = {2}

    • D. 

      D(S) = {0, 2}; R(S) = {0, 2, -2}

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