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