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