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WorksheetsSet Theory Quiz
Total questions: 30
Worksheet time: 16mins
What is a set?
A random assortment of items
A collection of well-defined objects
A group of people
A mathematical equation
What symbol indicates membership in a set?
⊆
∉
⊂
∈
What is a proper subset?
A set that contains some but not all elements of another set
A set that is equal to another set
A set with no elements
A set that contains all elements of another set
What is the null set?
A set that contains all elements
A set that is infinite
A set with no elements
A set with at least one element
What is the power set of a set A?
The set of all elements in A
The set of all subsets of A
The set of elements not in A
The set of elements in A and B
What does the union of two sets A and B represent?
Elements in A but not in B
Elements in A or B or both
Elements in B but not in A
Elements common to both A and B
What is the intersection of two sets A and B?
Elements in A but not in B
Elements in A and B
Elements in A or B
Elements in B but not in A
What does the symbol A - B represent?
The union of A and B
The intersection of A and B
The complement of A
The difference of A and B
What is the Cartesian product of sets A and B?
A set of all elements in B
A set of all pairs (a, b) where a is in A and b is in B
A set of all subsets of A
A set of all elements in A
What does the inclusion-exclusion principle help to calculate?
The number of elements in the intersection of two sets
The number of elements in a null set
The number of elements in the union of two sets
The number of elements in a proper subset
If A = {1, 2, 3} and B = {2, 3, 4}, what is A ∩ B?
{1, 4}
{1, 2, 4}
{2, 3}
{1, 2, 3}
What is the complement of a set A?
Only the elements in A
All elements in A
All elements not in A
The intersection of A with the universal set
What is the result of A ∪ ∅?
A ∩ ∅
U
∅
A
What is the result of A ∩ U?
A
U
∅
A ∪ U
Which of the following is true about disjoint sets?
They have no elements in common
They have at least one element in common
They are equal
They are subsets of each other
What does De Morgan's law state about the complement of a union?
The complement of a union is the intersection of the complements
The complement of a union is the union of the complements
The union of a complement is the complement of the union
The intersection of a complement is the union of the intersection
If A = {1, 2, 3} and B = {3, 4, 5}, what is A - B?
{1, 2}
{3}
{4, 5}
{1, 2, 3, 4, 5}
What is the cardinality of the power set of a set with n elements?
n!
n^2
2^n
n
In a Venn diagram, what does the overlapping region represent?
The difference of the sets
The intersection of the sets
The union of the sets
The complement of the sets
If x ∈ N and x is prime, then x is ________ set.
Infinite set
Finite set
Empty set
Not a set
What is the intersection of the power set of A and the power set of B?
The power set of A ∩ B
The empty set
The power set of B
The power set of A
Which of the following represents the complement of a set B?
All elements in the universal set
Elements in A
Elements in B
Elements not in B
If A = {x | x is an even number} and B = {x | x is a prime number}, what is A ∩ B?
∅
{3}
{2, 4, 6}
{2}
The members of the set S = {x | x is the square of an integer
and x < 100} is ________________
{0, 2, 4, 5, 9, 55, 46, 49, 99, 81}
{1, 4, 9, 16}
{0, 1, 4, 9, 16, 25, 36, 49, 64, 81}
{0, 1, 4, 9, 25, 36, 49, 123}
In a class of 40 students, 20 took Mathematics, 18 took Statistics, 16 took English, 7 took Mathematics and Statistics, 7 took Mathematics and English, 9 took Statistics and English, and 3 took all three courses. How many students are not taking any of these courses?
3
4
5
6
In a survey, it is found that in a particular locality 64 houses buy English newspapers, 94 houses buy Hindi newspapers, and 26 houses buy both English and Hindi newspapers. How many houses buy newspapers of only one language?
132
106
102
128
Consider the following sets: A = {x ∈ N | x mod 2 = 0 and 1 ≤ x ≤ 10} B = {x ∈ N | x mod 5 = 0 and 6 ≤ x ≤ 25} C = {x ∈ N | x mod 7 = 0 and 7 ≤ x ≤ 29} What is the cardinality of (A \ (B ∪ C)) ∪ (B \ (C ∪ A)) ∪ (C \ (B ∪ A))?
9
10
11
12
Which of the following statements about the set difference operation is/are correct? Let A and B be two sets. (1) A \ B contains all elements of A that are not in B.
(2) A \ B = B \ A if and only if A = B.
(3) A \ (B \ C) = (A \ B) ∪ (A ∩ C).
(4) (A \ B) ∩ (B \ A) = ∅.
1 and 3
2 and 4
1,3 and 4
1,2,3 and 4
The cardinality of the set of even positive integers less than
20 is__________?
8
10
9
12
Which of the following is a subset of set {1, 2, 3, 4}?
{1, 2}
{1, 2, 3}
{1}
All of the mentioned
