Mathematics for IGCSE & O level - Sets (Section 2)
1
How is the set {1, 2, 3, 4} written in roster notation?
إجابة
(B)
{1, 2, 3, 4}
2
Which of the following is an example of a finite set?
إجابة
(C)
The set of all days in a week.
3
Which set operation is represented by the shaded region in a Venn diagram where two overlapping circles are shown, and only the area of one circle is shaded?
إجابة
(D)
Set difference
4
If A = {1, 2, 3, 4, 5} and B = {4, 5, 6, 7, 8}, then what is A ∪ B (the union of A and B)?
إجابة
(C)
{1, 2, 3, 4, 5, 6, 7, 8}
5
Which of the following are ways to define a set?
إجابة
A
B
C
6
Which of the following best describes the meaning of n(A) in the context of sets?
إجابة
(B)
The number of elements in set A
7
What does the set difference, A - B, represent?
إجابة
(A)
All elements in A that are not in B.
8
Which of the following are true about sets?
إجابة
(C)
A set can contain an infinite number of elements.
9
Which of the following sets is empty?
إجابة
(C)
The set of all triangles with four sides.
10
If A = {1, 2, 3} and B = {3, 4, 5}, find (A ∪ B) ∩ {3, 4, 5, 6}.
إجابة
(A)
{3, 4, 5}
11
What is the cardinal number of the empty set?
إجابة
(A)
0
12
If A = {x | x is an even number} and B = {x | x is a multiple of 4}, then what is the relationship between A and B?
إجابة
(B)
B ⊆ A
13
Which of the following are characteristics of a Venn diagram?
إجابة
A
B
C
14
What is the value of n(A ∪ B) if n(A) = 10, n(B) = 8, and n(A ∩ B) = 3?
إجابة
(B)
18
15
What does the symbol ⊈ mean in set notation?
إجابة
(B)
Is not a subset of
16
If the universal set U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and set A = {2, 4, 6, 8, 10}, what is A' (the complement of A)?
إجابة
(A)
{1, 3, 5, 7, 9}
17
What is the definition of a set?
إجابة
(A)
A collection of shapes, letters, points or other objects.
18
If set A = {a, b, c} and set B = {d, e, f}, what is A ∩ B?
إجابة
(B)
{ }
19
In a class of 30 students, 15 like apples, 10 like bananas, and 5 like both. How many students like either apples or bananas (or both)?
إجابة
(B)
25
20
If set A has 5 elements, how many subsets does it have?
إجابة
(D)
32
21
In a Venn diagram, what is the area outside of all circles representing sets, but inside the rectangle (representing the universal set) represent?
إجابة
(B)
The complement of the union of the sets.
22
If there are 32 students in a class, and 18 study history and 20 study geography, and no student studies neither, how many students study BOTH history and geography?
إجابة
(C)
6
23
What does it mean for a set 'A' to be a subset of set 'B'?
إجابة
(A)
All elements of A are also elements of B
24
If A = {1, 2, 3} and B = {2, 3, 4, 5}, which number is NOT an element of A ∪ B?
إجابة
(D)
6
25
If A and B are disjoint sets, what is A ∩ B?
إجابة
(D)
The empty set
26
In a class of 40 students, 20 play football, 15 play basketball, and 10 play both. How many students play only one of these sports?
إجابة
(B)
25
27
In the study of sets, which of the following statements are generally true?
إجابة
(C)
Sets can be finite or infinite.
28
If U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A = {1, 2, 3, 4, 5} and B = {5, 6, 7}. Find A' ∪ B
إجابة
(B)
{5, 6, 7, 8, 9, 10}
29
If A = {1, 2, 3, 4} and B = {3, 4, 5, 6}. What does A - B represents?
إجابة
(A)
{1, 2}
30
What set is represented by the notation {x | x is a day of the week}?
إجابة
(C)
The set of all days of the week.
31
Which statement is an example of De Morgan's Law?
إجابة
(B)
(A ∪ B)' = A' ∩ B'
32
Which of the following is an example of a finite set?
إجابة
(C)
The set of all days of the week
33
Which of the following notations represents the set difference of A and B?
إجابة
(C)
A - B
34
The complement of a set A (denoted A') contains:
إجابة
(B)
Elements not in A
35
The intersection of two sets A and B is the set of all elements that are ________.
إجابة
(B)
In A and B
36
Which of the following is the correct way to represent 'x is not an element of set A'?
إجابة
(B)
x ∉ A
37
The symbol ℰ represents the ________ set.
إجابة
(B)
Universal
38
If A ⊆ B, and x ∈ A, then which of the following MUST be true?
إجابة
(B)
x ∈ B
39
Given sets A, B, and C, which of the following is associative?
إجابة
(B)
(A ∩ B) ∩ C = A ∩ (B ∩ C)
40
If U = {1, 2, 3, 4, 5, 6}, A = {1, 2, 3}, and B = {3, 4, 5}, what is (A ∪ B)'?
إجابة
(A)
{6}
41
In a Venn diagram, other sets are shown as ________ or similar.
إجابة
(C)
Circles
42
Which of the following operations is performed first in the order of operations related to sets?
إجابة
(A)
Complement
43
What is the name given to sets that do not share any common elements?
إجابة
(C)
Disjoint sets
44
Which Venn diagram shows two sets, P and Q, where there are no elements that are in both sets?
إجابة
(B)
Two separate circles
45
If U = {1, 2, 3, 4, 5}, A = {1, 2}, and B = {2, 3, 4}, what is (A ∩ B)'?
إجابة
(B)
{1, 3, 4, 5}
46
If A = {a, b, c} and B = {c, d, e}, what is (A ∪ B)' if the universal set is {a, b, c, d, e, f}?
إجابة
(B)
{f}
47
Which of the following statements about the empty set (Ø) is FALSE?
إجابة
(C)
The empty set is the complement of the universal set.
48
The set { } is also known as the _______ set.
إجابة
(C)
Empty
49
Which of the following is the correct symbol for 'is a subset of'?
إجابة
(B)
⊆
50
If A = {1, 3, 5} and B = {2, 4, 6}, which of the following correctly describes A and B?
