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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?
Answer
(B)
45
2
If n(A) = 5 and n(B) = 7, what is the maximum possible value of n(A ∪ B)?
Answer
(C)
12
3
Consider the sets: A = {1, 2, 3, 4}, B = {3, 4, 5, 6}. Which of the following is/are TRUE?
Answer
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?
Answer
(C)
A ∩ B
5
Which of the following is not a way to define a set?
Answer
(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?
Answer
(B)
{2, 3}
7
If n(A) = 7, n(B) = 9 and n(A ∩ B) = 4, what is n(A ∪ B)?
Answer
(B)
16
8
Which of these is an example of a set defined by a rule?
Answer
(C)
{x | x is an even number}
9
What is the result of A ∩ Ø, where Ø is the empty set?
Answer
(B)
Ø
10
If A = {red, green, blue} and B = {blue, yellow, orange}, what is the result of A - B?
Answer
(A)
{red, green}
11
Which of the following would contain all the elements in set P and all the elements in set Q?
Answer
(B)
P ∪ Q
12
What is the meaning of the symbol ∩?
Answer
(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 = ?
Answer
(A)
{a, p}
14
In a Venn diagram, how many sections are created by the intersection of three sets?
Answer
(D)
8
15
What is the meaning of the symbol ∪?
Answer
(B)
Union of sets
16
Venn diagrams are a way of showing ________ between sets.
Answer
(C)
Relationships
17
If A = {1, 2, 3} and B = {3, 1, 2}, what is the relationship between A and B?
Answer
(C)
A = B
18
If A = {1, 2, 3} and B = {3, 4, 5}, then A ∪ B is equal to:
Answer
(B)
{1, 2, 3, 4, 5}
19
If set A = {1, 2, 3} and set B = {4, 5, 6}, which statement is true?
Answer
(B)
A ∩ B = {}
20
What is the term for a set that contains an infinite number of elements?
Answer
(B)
Infinite set
21
In the context of set theory, what does the notation '∉' mean?
Answer
(B)
Is not an element of
22
If A = {1, 2, 3} and B = {3, 4, 5}, then A ∩ B is equal to:
Answer
(A)
{3}
23
If A and B are disjoint sets, what is A ∩ B?
Answer
(C)
{}
24
In a survey, 60 people like coffee, 50 like tea, and 30 like both. How many people like coffee or tea?
Answer
(A)
80
25
If A = {1, 2, 3, 4, 5} and B = {5, 6, 7}, what is A ∪ B?
Answer
(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?
Answer
(C)
P
27
If A = {1, 2, 3} and the universal set U = {1, 2, 3, 4, 5}, then A' is:
Answer
(B)
{4, 5}
28
How many subsets does a set with three elements have?
Answer
(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?
Answer
(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?
Answer
(C)
(P ∪ Q)'
31
What does it mean when a set is described as a 'finite set'?
Answer
(C)
The set has a definite, limited number of elements.
32
What is the result of the following set operation: A ∪ (A ∩ B)?
Answer
(A)
A
33
In a Venn diagram, the universal set is shown by a ________.
Answer
(B)
Rectangle
34
If A is a subset of B (A ⊆ B), what does this mean?
Answer
(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?
Answer
(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?
Answer
(B)
12
37
A set is a collection of ________.
Answer
(A)
Numbers, shapes, letters, points or other objects
38
If A ⊆ B, which of the following is ALWAYS true?
Answer
(D)
A ∪ B = B
39
Which of the following are correct regarding how to define a set?
Answer
A
B
40
If P and Q are disjoint sets, then:
Answer
(C)
P ∩ Q = Ø
41
Which of the following describes the number of subsets a set can have?
Answer
(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?
Answer
(C)
20
43
Which of the following statements is/are true about subsets?
Answer
A
B
C
44
Which statement is true about the intersection of a set and its complement?
Answer
(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?
Answer
(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?
Answer
(B)
45
47
Which of the following is not a property of set operations?
Answer
(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?
Answer
(B)
40
49
Which of the following represents the De Morgan's Law?
Answer
(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)')?
Answer
(A)
5