Mathematics for IGCSE & O level - Sets (Section 3)
1
How many students study at least one subject in this scenario: 25 students study history, 20 study geography, and 10 study both?
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(B)
45
2
If n(A) = 5 and n(B) = 7, what is the maximum possible value of n(A ∪ B)?
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(C)
12
3
Consider the sets: A = {1, 2, 3, 4}, B = {3, 4, 5, 6}. Which of the following is/are TRUE?
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A
B
D
4
What does the shaded region represent in a Venn diagram that consists of two overlapping circles if the shaded region includes only the area of the intersection?
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(C)
A ∩ B
5
Which of the following is not a way to define a set?
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(D)
Giving an example of an element in the set.
6
If the universal set is positive integers less than 5, and A = {prime numbers}, what are the elements of A?
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(B)
{2, 3}
7
If n(A) = 7, n(B) = 9 and n(A ∩ B) = 4, what is n(A ∪ B)?
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(B)
16
8
Which of these is an example of a set defined by a rule?
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(C)
{x | x is an even number}
9
What is the result of A ∩ Ø, where Ø is the empty set?
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(B)
Ø
10
If A = {red, green, blue} and B = {blue, yellow, orange}, what is the result of A - B?
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(A)
{red, green}
11
Which of the following would contain all the elements in set P and all the elements in set Q?
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(B)
P ∪ Q
12
What is the meaning of the symbol ∩?
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(C)
Intersection of sets
13
If A = {x | x is a letter in the word 'apple'} and B = {x | x is a letter in the word 'banana'}, then A ∩ B = ?
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(A)
{a, p}
14
In a Venn diagram, how many sections are created by the intersection of three sets?
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(D)
8
15
What is the meaning of the symbol ∪?
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(B)
Union of sets
16
Venn diagrams are a way of showing ________ between sets.
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(C)
Relationships
17
If A = {1, 2, 3} and B = {3, 1, 2}, what is the relationship between A and B?
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(C)
A = B
18
If A = {1, 2, 3} and B = {3, 4, 5}, then A ∪ B is equal to:
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(B)
{1, 2, 3, 4, 5}
19
If set A = {1, 2, 3} and set B = {4, 5, 6}, which statement is true?
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(B)
A ∩ B = {}
20
What is the term for a set that contains an infinite number of elements?
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(B)
Infinite set
21
In the context of set theory, what does the notation '∉' mean?
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(B)
Is not an element of
22
If A = {1, 2, 3} and B = {3, 4, 5}, then A ∩ B is equal to:
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(A)
{3}
23
If A and B are disjoint sets, what is A ∩ B?
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(C)
{}
24
In a survey, 60 people like coffee, 50 like tea, and 30 like both. How many people like coffee or tea?
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(A)
80
25
If A = {1, 2, 3, 4, 5} and B = {5, 6, 7}, what is A ∪ B?
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(B)
{1, 2, 3, 4, 5, 6, 7}
26
Which set operation is represented by the shaded region in a Venn diagram where the shaded area includes only the area of set P?
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(C)
P
27
If A = {1, 2, 3} and the universal set U = {1, 2, 3, 4, 5}, then A' is:
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(B)
{4, 5}
28
How many subsets does a set with three elements have?
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(C)
8
29
Which of the following would represent the shaded area if the shaded area in the Venn diagram includes everything in set P but exclude everything in set Q?
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(C)
P \ Q
30
What does the shaded area in a Venn diagram represent if P and Q are two sets and the shaded area covers everything outside of both sets?
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(C)
(P ∪ Q)'
31
What does it mean when a set is described as a 'finite set'?
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(C)
The set has a definite, limited number of elements.
32
What is the result of the following set operation: A ∪ (A ∩ B)?
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(A)
A
33
In a Venn diagram, the universal set is shown by a ________.
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(B)
Rectangle
34
If A is a subset of B (A ⊆ B), what does this mean?
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(A)
All elements of A are also in B
35
Given: U = {a, b, c, d, e}, A = {a, b}, B = {c, d}. What is A' ∩ B?
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(B)
{c, d}
36
In a class of 40 students, 20 study physics, 18 study chemistry, and 8 study both. How many students study neither physics nor chemistry?
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(B)
12
37
A set is a collection of ________.
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(A)
Numbers, shapes, letters, points or other objects
38
If A ⊆ B, which of the following is ALWAYS true?
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(D)
A ∪ B = B
39
Which of the following are correct regarding how to define a set?
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A
B
40
If P and Q are disjoint sets, then:
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(C)
P ∩ Q = Ø
41
Which of the following describes the number of subsets a set can have?
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(B)
2^n
42
In a class of 50 students, 30 play football, 25 play basketball, and 10 play both. How many students play only football?
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(C)
20
43
Which of the following statements is/are true about subsets?
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A
B
C
44
Which statement is true about the intersection of a set and its complement?
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(C)
It is the empty set.
45
Which of the following correctly describes the relationship between the sets represented in a Venn diagram where one circle is fully contained within another circle?
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(B)
One set is a subset of the other.
46
If a set has 10 elements, how many of its subsets will have 2 elements?
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(B)
45
47
Which of the following is not a property of set operations?
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(D)
Non-commutativity of intersection
48
In a survey of 50 students, 20 like apples, 25 like bananas, and 10 like both. How many students like either apples or bananas?
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(B)
40
49
Which of the following represents the De Morgan's Law?
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(C)
(A ∪ B)' = A' ∩ B'
50
If n(U) = 20, n(A) = 8, and n(B) = 10, and n(A ∩ B) = 3, what is n((A ∪ B)')?
