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Mathematics for IGCSE & O level - Sets (Section 1)

1
What are the characteristics of the empty set?
Answer
A
B
2
What does the term 'power set' of a set refer to?
Answer
(A)
The set of all subsets of the original set.
3
Given the universal set U = {1, 2, 3, 4, 5} and sets A = {1, 2} and B = {3, 4}. What is (A ∪ B)'?
Answer
(A)
{5}
4
Which of the following symbols is used to represent 'is not a subset of'?
Answer
(B)
⊈
5
When drawing Venn diagrams, what does the rectangle usually represent?
Answer
(C)
The universal set.
6
What does it mean to say set A is a subset of set B (A ⊆ B)?
Answer
A
D
7
If set A is {1, 2, 3, 4, 5} and set B is {4, 5, 6, 7, 8}. What is the set A ∩ B (intersection)?
Answer
(D)
{4, 5}
8
What is a set's complement relative to the universal set?
Answer
(C)
The set of elements in the universal set but not in the original set.
9
What is represented by the shaded area in a Venn diagram showing the union of two sets, A and B?
Answer
(B)
A ∪ B
10
What can be said about two sets if their union equals one of the sets?
Answer
(B)
One is a subset of the other.
11
Given the set P = {1, 2, 3, 4} and Q = {3, 4, 5, 6}, what is P ∩ Q (the intersection of P and Q)?
Answer
(C)
{3, 4}
12
Which of the following is equivalent to the set (A ∩ B)'?
Answer
(A)
A' ∪ B'
13
Which of the following statements about sets is correct?
Answer
A
C
14
Which statements describe properties of the empty set, represented by the symbol {} or ∅?
Answer
A
B
15
The notation {x | x > 5} represents which of the following?
Answer
(C)
The set of all numbers greater than 5.
16
If set A has 3 elements and set B has 4 elements, what is the maximum number of elements possible in A ∪ B?
Answer
(C)
7
17
What is the result when you take the intersection of a set with the universal set?
Answer
(B)
The set itself
18
What is the term for sets that contain no elements?
Answer
(C)
Empty sets
19
In the context of set theory, what does the notation P - Q mean?
Answer
(C)
All elements in P that are NOT in Q
20
Which of the following is true concerning the intersection of the set A and its complement, A'?
Answer
(D)
A ∩ A' = {} (Empty set)
21
If set A = {1, 2, 3} and the universal set U = {1, 2, 3, 4, 5}, what is A'?
Answer
(B)
{4, 5}
22
What is the relationship between two sets if their intersection results in the empty set?
Answer
(B)
They are disjoint sets.
23
If the set A = {1, 3, 5, 7} and B = {7, 9, 11}, what is A ∩ B?
Answer
(A)
{7}
24
If U = {1, 2, 3, 4, 5, 6} and A = {2, 4, 6}, what is A'?
Answer
(A)
{1, 3, 5}
25
If A = {1, 2, 3, 4} and B = {5, 6, 7}, what is A ∩ B?
Answer
(B)
{ }
26
Which of the following describes the intersection of sets A and B if A and B are the same set?
Answer
(B)
A
27
In a group of 40 students, 25 like English, 20 like Math, and 10 like both. How many students like neither English nor Math?
Answer
(A)
5
28
If A = {1, 2, 3}, then which of the following is a subset of A?
Answer
A
C
D
29
If P = {x | x is a multiple of 5} and Q = {10, 20, 30, 40, 50}, which of the following statements is true?
Answer
(B)
Q ⊆ P
30
Which of the following is true about disjoint sets?
Answer
(C)
They have no elements in common.
31
In a survey of 100 people, 60 like coffee, 40 like tea, and 20 like both. How many people like coffee OR tea?
Answer
(B)
80
32
Which of the following situations can be represented using set theory?
Answer
A
B
C
33
Which of the following is an example of a well-defined set?
Answer
(C)
The set of all prime numbers less than 20.
34
Which of the following accurately describes the meaning of the notation n(A)?
Answer
(C)
The number of elements in A.
35
In set theory, what does the notation P - Q (or P\Q) represent?
Answer
(B)
The set of all elements in P that are not in Q
36
In set notation, which symbol represents 'is an element of'?
Answer
(B)
∈
37
What operation is performed by the symbol ∁ in set notation?
Answer
(B)
Complement
38
Which of the following is true for all sets A, B and C?
Answer
A
B
C
39
In a Venn diagram, how would you represent the set (A ∩ B')?
Answer
(A)
The region inside circle A and outside circle B.
40
If set A = {a, b, c} and set B = {c, d, e}, what is A ∪ B?
Answer
(B)
{a, b, c, d, e}
41
In a survey of 50 students, 20 like Math, 25 like Science, and 10 like both. How many students like only Math?
Answer
(A)
10
42
Which of the following are examples of sets?
Answer
A
B
D
43
What is the intersection of sets P and Q when they are disjoint?
Answer
(C)
The empty set
44
Which of the following statements accurately describes two sets that are disjoint?
Answer
(B)
The sets share no elements in common.
45
Which symbol is used to represent 'not an element of'?
Answer
(B)
∉
46
What is the complement of the set of all prime numbers within the universal set of integers from 1 to 10?
Answer
(A)
{1, 4, 6, 8, 9, 10}
47
What is the meaning of A ⊆ B?
Answer
(B)
A is a subset of B or A = B
48
Given a 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)?
Answer
(A)
{1, 3, 5, 7, 9}
49
Which set operation describes the union of sets A and B?
Answer
(B)
The set of all elements belonging to either A or B (or both).
50
What is the result of P ∪ Q if P = {a, b, c} and Q = {c, d, e}?
Answer
(B)
{a, b, c, d, e}