Mathematics for IGCSE & O level - Sets (Section 2)
1
How is the set {1, 2, 3, 4} written in roster notation?
Απάντηση
(B)
{1, 2, 3, 4}
2
Which of the following is an example of a finite set?
Απάντηση
(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?
Απάντηση
(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)?
Απάντηση
(C)
{1, 2, 3, 4, 5, 6, 7, 8}
5
Which of the following are ways to define a set?
Απάντηση
A
B
C
6
Which of the following best describes the meaning of n(A) in the context of sets?
Απάντηση
(B)
The number of elements in set A
7
What does the set difference, A - B, represent?
Απάντηση
(A)
All elements in A that are not in B.
8
Which of the following are true about sets?
Απάντηση
(C)
A set can contain an infinite number of elements.
9
Which of the following sets is empty?
Απάντηση
(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}.
Απάντηση
(A)
{3, 4, 5}
11
What is the cardinal number of the empty set?
Απάντηση
(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?
Απάντηση
(B)
B ⊆ A
13
Which of the following are characteristics of a Venn diagram?
Απάντηση
A
B
C
14
What is the value of n(A ∪ B) if n(A) = 10, n(B) = 8, and n(A ∩ B) = 3?
Απάντηση
(B)
18
15
What does the symbol ⊈ mean in set notation?
Απάντηση
(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)?
Απάντηση
(A)
{1, 3, 5, 7, 9}
17
What is the definition of a set?
Απάντηση
(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?
Απάντηση
(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)?
Απάντηση
(B)
25
20
If set A has 5 elements, how many subsets does it have?
Απάντηση
(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?
Απάντηση
(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?
Απάντηση
(C)
6
23
What does it mean for a set 'A' to be a subset of set 'B'?
Απάντηση
(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?
Απάντηση
(D)
6
25
If A and B are disjoint sets, what is A ∩ B?
Απάντηση
(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?
Απάντηση
(B)
25
27
In the study of sets, which of the following statements are generally true?
Απάντηση
(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
Απάντηση
(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?
Απάντηση
(A)
{1, 2}
30
What set is represented by the notation {x | x is a day of the week}?
Απάντηση
(C)
The set of all days of the week.
31
Which statement is an example of De Morgan's Law?
Απάντηση
(B)
(A ∪ B)' = A' ∩ B'
32
Which of the following is an example of a finite set?
Απάντηση
(C)
The set of all days of the week
33
Which of the following notations represents the set difference of A and B?
Απάντηση
(C)
A - B
34
The complement of a set A (denoted A') contains:
Απάντηση
(B)
Elements not in A
35
The intersection of two sets A and B is the set of all elements that are ________.
Απάντηση
(B)
In A and B
36
Which of the following is the correct way to represent 'x is not an element of set A'?
Απάντηση
(B)
x ∉ A
37
The symbol ℰ represents the ________ set.
Απάντηση
(B)
Universal
38
If A ⊆ B, and x ∈ A, then which of the following MUST be true?
Απάντηση
(B)
x ∈ B
39
Given sets A, B, and C, which of the following is associative?
Απάντηση
(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)'?
Απάντηση
(A)
{6}
41
In a Venn diagram, other sets are shown as ________ or similar.
Απάντηση
(C)
Circles
42
Which of the following operations is performed first in the order of operations related to sets?
Απάντηση
(A)
Complement
43
What is the name given to sets that do not share any common elements?
Απάντηση
(C)
Disjoint sets
44
Which Venn diagram shows two sets, P and Q, where there are no elements that are in both sets?
Απάντηση
(B)
Two separate circles
45
If U = {1, 2, 3, 4, 5}, A = {1, 2}, and B = {2, 3, 4}, what is (A ∩ B)'?
Απάντηση
(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}?
Απάντηση
(B)
{f}
47
Which of the following statements about the empty set (Ø) is FALSE?
Απάντηση
(C)
The empty set is the complement of the universal set.
48
The set { } is also known as the _______ set.
Απάντηση
(C)
Empty
49
Which of the following is the correct symbol for 'is a subset of'?
Απάντηση
(B)
⊆
50
If A = {1, 3, 5} and B = {2, 4, 6}, which of the following correctly describes A and B?
