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