Mathematics for IGCSE & O level - Sets (Section 2)
1
How is the set {1, 2, 3, 4} written in roster notation?
Answer
(B)
{1, 2, 3, 4}
2
Which of the following is an example of a finite set?
Answer
(C)
The set of all days in a week.
3
Which set operation is represented by the shaded region in a Venn diagram where two overlapping circles are shown, and only the area of one circle is shaded?
Answer
(D)
Set difference
4
If A = {1, 2, 3, 4, 5} and B = {4, 5, 6, 7, 8}, then what is A ∪ B (the union of A and B)?
Answer
(C)
{1, 2, 3, 4, 5, 6, 7, 8}
5
Which of the following are ways to define a set?
Answer
A
B
C
6
Which of the following best describes the meaning of n(A) in the context of sets?
Answer
(B)
The number of elements in set A
7
What does the set difference, A - B, represent?
Answer
(A)
All elements in A that are not in B.
8
Which of the following are true about sets?
Answer
(C)
A set can contain an infinite number of elements.
9
Which of the following sets is empty?
Answer
(C)
The set of all triangles with four sides.
10
If A = {1, 2, 3} and B = {3, 4, 5}, find (A ∪ B) ∩ {3, 4, 5, 6}.
Answer
(A)
{3, 4, 5}
11
What is the cardinal number of the empty set?
Answer
(A)
0
12
If A = {x | x is an even number} and B = {x | x is a multiple of 4}, then what is the relationship between A and B?
Answer
(B)
B ⊆ A
13
Which of the following are characteristics of a Venn diagram?
Answer
A
B
C
14
What is the value of n(A ∪ B) if n(A) = 10, n(B) = 8, and n(A ∩ B) = 3?
Answer
(B)
18
15
What does the symbol ⊈ mean in set notation?
Answer
(B)
Is not a subset of
16
If the universal set U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and set A = {2, 4, 6, 8, 10}, what is A' (the complement of A)?
Answer
(A)
{1, 3, 5, 7, 9}
17
What is the definition of a set?
Answer
(A)
A collection of shapes, letters, points or other objects.
18
If set A = {a, b, c} and set B = {d, e, f}, what is A ∩ B?
Answer
(B)
{ }
19
In a class of 30 students, 15 like apples, 10 like bananas, and 5 like both. How many students like either apples or bananas (or both)?
Answer
(B)
25
20
If set A has 5 elements, how many subsets does it have?
Answer
(D)
32
21
In a Venn diagram, what is the area outside of all circles representing sets, but inside the rectangle (representing the universal set) represent?
Answer
(B)
The complement of the union of the sets.
22
If there are 32 students in a class, and 18 study history and 20 study geography, and no student studies neither, how many students study BOTH history and geography?
Answer
(C)
6
23
What does it mean for a set 'A' to be a subset of set 'B'?
Answer
(A)
All elements of A are also elements of B
24
If A = {1, 2, 3} and B = {2, 3, 4, 5}, which number is NOT an element of A ∪ B?
Answer
(D)
6
25
If A and B are disjoint sets, what is A ∩ B?
Answer
(D)
The empty set
26
In a class of 40 students, 20 play football, 15 play basketball, and 10 play both. How many students play only one of these sports?
Answer
(B)
25
27
In the study of sets, which of the following statements are generally true?
Answer
(C)
Sets can be finite or infinite.
28
If U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A = {1, 2, 3, 4, 5} and B = {5, 6, 7}. Find A' ∪ B
Answer
(B)
{5, 6, 7, 8, 9, 10}
29
If A = {1, 2, 3, 4} and B = {3, 4, 5, 6}. What does A - B represents?
Answer
(A)
{1, 2}
30
What set is represented by the notation {x | x is a day of the week}?
Answer
(C)
The set of all days of the week.
31
Which statement is an example of De Morgan's Law?
Answer
(B)
(A ∪ B)' = A' ∩ B'
32
Which of the following is an example of a finite set?
Answer
(C)
The set of all days of the week
33
Which of the following notations represents the set difference of A and B?
Answer
(C)
A - B
34
The complement of a set A (denoted A') contains:
Answer
(B)
Elements not in A
35
The intersection of two sets A and B is the set of all elements that are ________.
Answer
(B)
In A and B
36
Which of the following is the correct way to represent 'x is not an element of set A'?
Answer
(B)
x ∉ A
37
The symbol ℰ represents the ________ set.
Answer
(B)
Universal
38
If A ⊆ B, and x ∈ A, then which of the following MUST be true?
Answer
(B)
x ∈ B
39
Given sets A, B, and C, which of the following is associative?
Answer
(B)
(A ∩ B) ∩ C = A ∩ (B ∩ C)
40
If U = {1, 2, 3, 4, 5, 6}, A = {1, 2, 3}, and B = {3, 4, 5}, what is (A ∪ B)'?
Answer
(A)
{6}
41
In a Venn diagram, other sets are shown as ________ or similar.
Answer
(C)
Circles
42
Which of the following operations is performed first in the order of operations related to sets?
Answer
(A)
Complement
43
What is the name given to sets that do not share any common elements?
Answer
(C)
Disjoint sets
44
Which Venn diagram shows two sets, P and Q, where there are no elements that are in both sets?
Answer
(B)
Two separate circles
45
If U = {1, 2, 3, 4, 5}, A = {1, 2}, and B = {2, 3, 4}, what is (A ∩ B)'?
Answer
(B)
{1, 3, 4, 5}
46
If A = {a, b, c} and B = {c, d, e}, what is (A ∪ B)' if the universal set is {a, b, c, d, e, f}?
Answer
(B)
{f}
47
Which of the following statements about the empty set (Ø) is FALSE?
Answer
(C)
The empty set is the complement of the universal set.
48
The set { } is also known as the _______ set.
Answer
(C)
Empty
49
Which of the following is the correct symbol for 'is a subset of'?
Answer
(B)
⊆
50
If A = {1, 3, 5} and B = {2, 4, 6}, which of the following correctly describes A and B?
