O level Set Theory Quiz 1

15 Questions

Quiz Description

   In this quiz, we are going to focus on what a set is all about and the questions provided to you by gcequiz.com in this quiz, o level set theory quiz 1, have been set based on the national syllabus for the ordinary level.   

Set Theory is a limb of logic that studies what is known as a set. 

A Set is a collection of well defined objects.

Sets are generally subdivided into two, Finite sets and Infinite sets. There are other types of sets such as null sets, subsets, universal sets and so many other types of sets. Below, we're going to look at the definitions of some of these types of sets.

To test your knowledge on this particular aspect of ordinary level mathematics, you can go ahead and answer the quiz. 

Good Luck

1:

 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)


Correct
  • 1:
    R is relexive and transitive
  • 2:
    R is symmetric and not transitive
  • 3:
    R is an equivalence relation
  • 4:
    R is not relexive and not symmetric
2:

 Which of the following sets are null sets ?


Correct
  • 1:
    {0}
  • 2:
    ø
  • 3:
    { }
  • 4:
    Both (b) & (c)
3:

  Number of subsets of a set of order three is


Correct
  • 1:
    3
  • 2:
    6
  • 3:
    8
  • 4:
    9
4:

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


Correct
  • 1:
    A = Φ
  • 2:
    B = Φ
  • 3:
    A = B
  • 4:
    none of these
5:

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


Correct
  • 1:
    atleast one of the sets Si is a finite set
  • 2:
    atleast one of the sets Si is an ininite set
  • 3:
    not more than one of the set Si can be inite
  • 4:
    none of these
6:

 If X and Y are two sets, then X  ∩ (Y  ∪ X) C equals


Correct
  • 1:
    X
  • 2:
    Ø
  • 3:
    Y
  • 4:
    None of these
7:

  If  f : X -> Y and a, b  ⊆ X, then f (a  ∩ b) is equal to


Correct
  • 1:
    f(a) - f(b)
  • 2:
    a proper subset of f(a) ∩ f(b)
  • 3:
    f(a) ∩ f(b)
  • 4:
    f(b) - f(a)
8:

  The number of elements in the power set of the set {{a, b}, c} is


Correct
  • 1:
    8
  • 2:
    4
  • 3:
    3
  • 4:
    7
9:

 In a language survey of students it is found that 80 students know English, 60 know French, 50 know German, 30 known English and French, 20 know French and German, 15 know English and German and 10 students know all the three languages.

How many students know at least one language?


Correct
  • 1:
    135
  • 2:
    30
  • 3:
    10
  • 4:
    45
10:

 In a room containing 28 people, there are 18 people who speak English, 15 people who speak Hindi and 22 people who speak Kannada, 9 persons speak both English and Hindi, 11 persons speak both Hindi and Kannada where as 13 persosn speak both Kannada and English. How many people speak all the three languages ? 


Correct
  • 1:
    6
  • 2:
    7
  • 3:
    8
  • 4:
    9
11:

 In a beauty contest, half the number of experts voted for Mr. A and two thirds voted for Mr. B. 10 voted for both and 6 did not vote for either. How many experts were there in all ? 


Correct
  • 1:
    18
  • 2:
    36
  • 3:
    24
  • 4:
    None of these
12:

 Let n(A) denotes the number of elements in set A. If n(A) =p and n(B) = q, then how many ordered pairs (a, b) are there with a ∈ A and b ∈ B ? 


Correct
  • 1:
    p^2
  • 2:
    p x q
  • 3:
    p + q
  • 4:
    2 pq
13:

 If f : R ---->R defined by f(x) = x2 + 1, then values of f -1 (17) and  f -1(-3) are respectively 


Correct
  • 1:
    {Ø}, (4, - 4)
  • 2:
    {3,-3},{Ø}
  • 3:
    {Ø},{3,-3}
  • 4:
    {4,-4},Ø
14:

 The set of all Equivalence classes of a set A of cardinality C


Correct
  • 1:
    has the same cardinality as A
  • 2:
    forms a partition of A
  • 3:
    is of cardinality 2C
  • 4:
    is of cardinality C^2
15:

 Let x and y are sets and I x I and l y I are their respective cardinalities. It is given that there are exactly 97 functions from x to y. From this one can conclude that  


Correct
  • 1:
    │x│ = 1, │y│ = 97
  • 2:
    │x│ = 97, │y│= 1
  • 3:
    │x│ = 97, │y│= 97
  • 4:
    none of these

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O level Set Theory Quiz 1
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