Mathematics for IGCSE & O level - Sets (Section 2)
1
How is the set {1, 2, 3, 4} written in roster notation?
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(B)
{1, 2, 3, 4}
2
Which of the following is an example of a finite set?
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(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?
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(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)?
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(C)
{1, 2, 3, 4, 5, 6, 7, 8}
5
Which of the following are ways to define a set?
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A
B
C
6
Which of the following best describes the meaning of n(A) in the context of sets?
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(B)
The number of elements in set A
7
What does the set difference, A - B, represent?
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(A)
All elements in A that are not in B.
8
Which of the following are true about sets?
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(C)
A set can contain an infinite number of elements.
9
Which of the following sets is empty?
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(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}.
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(A)
{3, 4, 5}
11
What is the cardinal number of the empty set?
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(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?
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(B)
B ⊆ A
13
Which of the following are characteristics of a Venn diagram?
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A
B
C
14
What is the value of n(A ∪ B) if n(A) = 10, n(B) = 8, and n(A ∩ B) = 3?
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(B)
18
15
What does the symbol ⊈ mean in set notation?
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(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)?
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(A)
{1, 3, 5, 7, 9}
17
What is the definition of a set?
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(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?
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(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)?
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(B)
25
20
If set A has 5 elements, how many subsets does it have?
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(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?
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(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?
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(C)
6
23
What does it mean for a set 'A' to be a subset of set 'B'?
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(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?
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(D)
6
25
If A and B are disjoint sets, what is A ∩ B?
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(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?
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(B)
25
27
In the study of sets, which of the following statements are generally true?
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(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
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(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?
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(A)
{1, 2}
30
What set is represented by the notation {x | x is a day of the week}?
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(C)
The set of all days of the week.
31
Which statement is an example of De Morgan's Law?
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(B)
(A ∪ B)' = A' ∩ B'
32
Which of the following is an example of a finite set?
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(C)
The set of all days of the week
33
Which of the following notations represents the set difference of A and B?
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(C)
A - B
34
The complement of a set A (denoted A') contains:
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(B)
Elements not in A
35
The intersection of two sets A and B is the set of all elements that are ________.
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(B)
In A and B
36
Which of the following is the correct way to represent 'x is not an element of set A'?
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(B)
x ∉ A
37
The symbol ℰ represents the ________ set.
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(B)
Universal
38
If A ⊆ B, and x ∈ A, then which of the following MUST be true?
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(B)
x ∈ B
39
Given sets A, B, and C, which of the following is associative?
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(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)'?
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(A)
{6}
41
In a Venn diagram, other sets are shown as ________ or similar.
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(C)
Circles
42
Which of the following operations is performed first in the order of operations related to sets?
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(A)
Complement
43
What is the name given to sets that do not share any common elements?
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(C)
Disjoint sets
44
Which Venn diagram shows two sets, P and Q, where there are no elements that are in both sets?
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(B)
Two separate circles
45
If U = {1, 2, 3, 4, 5}, A = {1, 2}, and B = {2, 3, 4}, what is (A ∩ B)'?
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(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}?
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(B)
{f}
47
Which of the following statements about the empty set (Ø) is FALSE?
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(C)
The empty set is the complement of the universal set.
48
The set { } is also known as the _______ set.
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(C)
Empty
49
Which of the following is the correct symbol for 'is a subset of'?
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(B)
⊆
50
If A = {1, 3, 5} and B = {2, 4, 6}, which of the following correctly describes A and B?
