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