Set Notation & Venn Diagrams (Edexcel IGCSE Maths)

Exam Questions

2 hours37 questions
1a
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2 marks

A = {p, r, a, g, u, e}

B = {p, a, r, i, s}

C = {b, u, d, a, p, e, s, t}

List the members of the set

i)
AB,
[1]

ii)
B C.

[1]

1b
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1 mark

D = {r, o, m, e}

E = {l, i, s, b, o, n}

F = {b, e, r, l, i, n}

Put one of the letters D, E or F in the box below to make the statement correct.

q1b-set-diagrams-and-venn-diagrams-easy-edexcel-igcse-maths

Explain your answer.

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2a
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2 marks

ξ = {even numbers}

A = {2, 4, 6, 8, 10}           

B is a set such that AB = {4, 8}
The set B has 3 members. 

List the members of one possible set B.

2b
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1 mark

C is a set such that AC =
The set C has 3 members.

List the members of one possible set C.

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3a
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1 mark

S = {c, h, i, n, a}

V = {i, t, a, l, y}

List the elements of the set

S intersection V

3b
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1 mark

union V

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4a
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1 mark

xi = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

A = {1, 2, 3, 4, 5, 6}

B = {odd numbers}

Find n(A union B)

4b
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2 marks

C is a set such that intersection C = {4, 5}
The set C has 4 members

List the members of one possible set C.

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5
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3 marks

In a survey of 50 people,

30 owned a cat
25 owned a dog
6 owned neither a cat or a dog

Complete the Venn diagram to show this information.

q9a-set-diagrams-and-venn-diagrams-easy-edexcel-igcse-maths

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6
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2 marks

calligraphic E = {20, 21, 22, 23, 24, 25, 26, 27, 28, 29}

A = {odd numbers}

B = {multiples of 3}

List the members of the set

i)
A space intersection space B

[1]
ii)
A space union space B
[1]

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7a
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2 marks

calligraphic E = {21, 22, 23, 24, 25, 26, 27, 28, 29, 30}

A = {22, 24, 26, 28, 30}

B = {21, 24, 27, 30}

List the members of the set

i)
A space intersection space B
[1]


ii)
A apostrophe

[1]
7b
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1 mark

C = {23, 25, 29}

Using set notation, find an expression for C in terms of A and B.

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8a
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2 marks

calligraphic E= {letters of the alphabet}
B = {b, r, a, z, i, l}
I = {i, r, e, l, a, n, d}

List the members of the set

i)
B space union space I
[1]

ii)
B space intersection space I ʹ
[1]
8b
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1 mark

K = {k, e, n, y, a}

Cody writes down the statement B space intersection space K space equals space empty set
Cody’s statement is wrong.

Explain why.

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9a
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2 marks

table attributes columnalign right center left columnspacing 0px end attributes row B equals cell open curly brackets straight b comma straight l comma straight u comma straight e close curly brackets end cell row G equals cell open curly brackets straight g comma straight r comma straight e comma straight y close curly brackets end cell row W equals cell open curly brackets straight w comma straight h comma straight i comma straight t comma straight e close curly brackets end cell end table

List all the members of the set


i)
B space union space G
[1]
ii)
W space intersection space G prime
[1]
9b
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1 mark

Serena writes down the statement B space intersection space G space intersection space W space equals space empty set

Is Serena’s statement correct?
You must give a reason for your answer.

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10
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2 marks

The numbers from 1 to 14 are shown in the Venn diagram.

q1-paper1h-nov2020-edexcel-igcse-maths

i)
List the members of the set A intersection B

[1]

ii)
List the members of the set B ʹ 

[1]

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11a
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1 mark

table attributes columnalign right center left columnspacing 0px end attributes row cell calligraphic E space end cell equals cell space open curly brackets 1 comma 2 comma 3 comma 4 comma 5 comma 6 comma 7 comma 8 comma 9 comma 10 close curly brackets end cell row cell A space end cell equals cell space open curly brackets 2 comma 3 comma 5 comma 7 close curly brackets end cell row cell B space end cell equals cell thin space open curly brackets 4 comma 6 comma 8 comma 10 close curly brackets end cell end table

Explain why A space intersection space B space equals space empty set

11b
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1 mark

x space element of space calligraphic E spaceand x space not an element of space A union space B

Write down the two possible values of space x.

11c
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2 marks

Set C is such that

table row cell A space union space B space union space C space end cell equals cell space calligraphic E end cell row cell A space intersection space C space end cell equals cell space open curly brackets 2 close curly brackets end cell row cell B space intersection space C apostrophe space end cell equals cell space open curly brackets 4 space comma space 6 space comma space 10 close curly brackets end cell row blank blank blank end table

List all the members of set C.

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1
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2 marks

ξ = {even numbers}

A = {factors of 8}

B = {factors of 20}

List the members of the set AB.

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2a
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1 mark

ξ = {Students in year 12}

G = {Students who study German}

F = {Students who study French}

M = {Students who study Maths}

GM = ∅

Use this information to write a statement about the students who study German in Year 12.

2b
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1 mark

Preety is a student in Year 12,

Preety ∉ F.

Use this information to write a statement about Preety.

2c
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2 marks

A = {2, 4, 6, 8, 10}

AB = {2, 4} 

A B = {1, 2, 3, 4, 6, 8, 10}

List all the members of set B.

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3a
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2 marks

A = {s, u, p, e, r}

B = {c, o, m, p, u, t, e, r}

List the members of the set

i)
AB,
[1]
ii)
A B.
[1]
3b
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1 mark

X = {prime numbers}

Y = {factors of 12}

Is it true that XY = ∅?

Tick (✔) the appropriate box.

◻  Yes           ◻ No

Explain your answer.

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4
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1 mark

ξ = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}

A = {odd numbers}

P = {prime number}

List the members of the set AP.

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5a
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2 marks

A, B and C are three sets.

AB = ∅ and C ⊂ A

qp5a-1-2-medium-edexcel-igcse-maths

Complete the Venn diagram to show the sets B and C.

5b
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1 mark

On the Venn diagram, shade the region that represents AC’.

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6a
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1 mark

The Venn diagram shows a universal set ξ and three sets A, B and C.

q6a-1-2-medium-edexcel-igcse-maths

7, 6, 3, 2 and 10 represent the number of elements in each set.

Find

n(AB)

6b
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1 mark

n(A’)

6c
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1 mark

n(BC’)

6d
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1 mark

n(A’ B’)

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7
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2 marks

ξ = {whole numbers}

A = {factors of 100}

B = {multiples of 5}

List the members of the set AB.

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8a
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1 mark

ξ = {1, 2, 3, 4, 5, 6, 7, 8, 9}

A = {1, 3, 5, 7}

B = {2, 4, 6, 8}

Explain why AB = ∅.

8b
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1 mark

xξ and xA B.

Write down the value of x.

x = ……………………………………… 

8c
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2 marks

AC = {3, 7}, BC = {8} and A B C = ξ.

List all the members of C.

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9a
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2 marks

ξ = {positive whole numbers less than 19}

A = {odd numbers}

B = {multiples of 5}

C = {multiples of 4}

List the members of the set

i)
AB’,

ii)
B C.
9b
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1 mark

D = {prime numbers}

Is it true that CD = ∅?

Tick (✔) the appropriate box.

◻ Yes       ◻ No

Explain your answer.

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10a
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1 mark

ξ = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

A = {even numbers}

B = {multiples of 3}

List the members of set B’.

10b
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1 mark

Find n(A’B).

10c
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2 marks

x is a member of ξ,

x B, 

x A.

What are the possible values of x?

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11a
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3 marks

A and B are two sets.

n(ξ) = 36

n(B) = 21

n(AB) = 8 

n(A’) = 18

Complete the Venn diagram to show the number of elements in each region.

q11a-1-2-medium-edexcel-igcse-maths

11b
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2 marks

Find

i)
n(AB)

ii)
n(A B’)

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12a
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2 marks

The Venn diagram shows a universal set ξ and three sets X, Y and Z.

q12a-1-2-medium-edexcel-igcse-maths

The numbers shown represent the numbers of elements.

n(X’) = 14

n(Z) = 14

Complete the Venn diagram.

12b
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2 marks

Find

i)
n(XZ)

ii)
n(X Y’)

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13a
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1 mark

The Venn diagram shows a universal set calligraphic E and three sets A comma space B and C.

q17-4ma1-1hr-qp-jan22-paper1-igcse-maths

6, 3, 8, 2, 5 and 4 represent the numbers of elements.

Find

straight n left parenthesis A space union space B right parenthesis

13b
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1 mark

straight n left parenthesis A space intersection space B right parenthesis

13c
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1 mark

straight n left parenthesis B space intersection space C apostrophe right parenthesis

13d
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1 mark

straight n left parenthesis A apostrophe space union space B apostrophe space union space C apostrophe right parenthesis

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14
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3 marks

The Venn diagram shows a universal set, calligraphic E and sets A comma space B and C.

q19-4ma1-1h-qp-june21-paper1-igcse-maths

12, 5, 9, 10, 6, 3, 4 and 8 represent the numbers of elements.

Find

i)
n left parenthesis A space union space B right parenthesis
[1]

ii)
n left parenthesis A ʹ space intersection space B ʹ right parenthesis
[1]

iii)
n left parenthesis left square bracket A space intersection space B right square bracket space union space C right parenthesis
[1]

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1a
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2 marks

A and B are two sets.

n(ξ) = 37

n(A) = 22

n(AB) = 12 

n(A B) = 30

Complete the Venn diagram to show the number of elements in each region.

94Zlu7G3_q11a-1-2-medium-edexcel-igcse-maths

1b
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2 marks

Find

i)
n(AB′)

ii)
n(A′ ∪ B′)

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2
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4 marks

There are 31 students in a class.

The only languages available for the class to study are French and Spanish.

17 students study French.

15 students study Spanish.

6 students study neither French not Spanish.

Using a Venn diagram, or otherwise, work out how many students study only one language.

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3
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4 marks

A garage tests cars for faults. 

There are three types of fault – braking, steering and lighting.

A car fails the test if it has one or more of these three types of fault.

Last week, 11 cars had breaking faults, 

                   9 cars had steering faults,

                   7 cars had lighting faults, 

                   no car had both steering faults and lighting faults, 

                   2 cars had both braking faults and steering faults, 

                   3 cars had both braking faults and lighting faults.

By drawing a Venn diagram, or otherwise, find the number of cars which failed the test last week.

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4a
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2 marks

ξ = {positive whole numbers less than 13}

A = {even numbers}

B = {multiples of 3}

C = {prime numbers}

List the members of the set

i)
A′ ∩ B′,

ii)
B C.
4b
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1 mark

Is it true that 14 ∈ A?

Tick (✔) the appropriate box.

◻ Yes         ◻ No

Explain your answer.

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5a
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1 mark

The Venn diagram shows a universal set ξ and three sets A, B and C.

q13a-1-2-hard-edexcel-igcse-maths

2, 4, 7, 3, 6 and 10 represent the number of elements in each set.

Find

n(AB)

5b
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1 mark

n(B′)

5c
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1 mark

n(AC′)

5d
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1 mark

n(B′ ∩ C′)

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6a
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1 mark

The Venn diagram shows all of the elements in sets A, B and ξ.

q6a-1-2-hard-edexcel-igcse-maths

Write down the elements in A′

6b
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1 mark

Find n(AB)′,

6c
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1 mark

Find the elements in (AB) ∪ (AB)′,

6d
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1 mark

AC = ∅

BC = {5, 6, 7, 8, 9}

n(C) = 3

Write down the elements in C.

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7a
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2 marks

On the Venn diagram, shade the set (AB) ∩ C′.

q6c-1-2-hard-edexcel-igcse-maths

7b
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2 marks

Use set notation to describe the shaded region in the Venn diagram below.

q6d-1-2-hard-edexcel-igcse-maths

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8a
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2 marks

ξ = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13}

A = {3, 7, 11, 13}

B = {3, 6, 9, 12, 13}

C = {2, 3, 5, 6, 7, 8}

Complete the Venn diagram

q8a-1-2-hard-edexcel-igcse-maths

8b
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1 mark

List the members of the set B′ C.

8c
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1 mark

List the members of the set (AC)′ ∩ B.

8d
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1 mark

Find n(A′B′)

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9
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3 marks

Each student in a group of 32 students was asked the following question.

“Do you have a desktop computer (D), a laptop (L) or a tablet (T)?”

Their answers showed that,

19 students have a desktop computer,

17 students have a laptop,

16 students have a tablet,

9 students have both a desktop computer and a laptop,

11 students have both a desktop computer and a tablet,

7 students have both a laptop and a tablet,

5 students have all three.

Using this information, complete the Venn diagram to show the number of students in each appropriate subset.

q9-1-2-hard-edexcel-igcse-maths

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10a
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3 marks

Some students were asked the following question.

“Which of the subjects Russian (R), French (F) and German (G) do you study?”

Of these students

4 study all three of Russian, French and German
10 study Russian and French
13 study French and German
6 study Russian and German
24 study German
11 study none of the three subjects
the number who study Russian only is twice the number who study French only.

Let x be the number of students who study French only.

Show all this information on the Venn diagram, giving the number of students in each appropriate subset, in terms of x where necessary.

q16a-4ma1-2h-qp-jan21-paper2-igcse-maths

10b
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3 marks

Given that the number of students who were asked the question was 80, work out the number of these students that study Russian.

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11
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3 marks

calligraphic E = {4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}

A intersection B = {5, 10, 15}

B apostrophe= {7, 8, 9, 11, 12, 13, 14}

A apostrophe= {4, 6, 7, 8, 14}

Complete the Venn diagram for this information.

q7-january-2022-1h-edexcel-igcse-maths

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12a
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3 marks

Some students in a school were asked the following question.

“Do you have a dog (D), a cat (C) or a rabbit (R)?”

Of these students

   28 have a dog
   18 have a cat
   20 have a rabbit
    8 have both a cat and a rabbit
    9 have both a dog and a rabbit
    x have both a dog and a cat
    6 have a dog, a cat and a rabbit
    5 have not got a dog or a cat or a rabbit

Using this information, complete the Venn diagram to show the number of students in each appropriate subset.
Give the numbers in terms of x where necessary.

q17a-ma1-2hr-qp-jan20-paper2-igcse-maths

12b
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2 marks

Given that a total of 50 students answered the question,

work out the value of x.

x = ........................

12c
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1 mark

Find  n left parenthesis C ʹ space intersection space D ʹ right parenthesis

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