O LevelMathsCambridgeExam QuestionsNumberSet Notation & Venn Diagrams

Set Notation & Venn Diagrams (Cambridge O Level Maths)

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Set Notation & Venn Diagrams

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Set Notation & Venn Diagrams

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1a
Sme Calculator2 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]

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1b
Sme Calculator1 mark

C = {23, 25, 29}

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

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2a
Sme Calculator2 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]

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2b
Sme Calculator1 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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3a
Sme Calculator2 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]

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3b
Sme Calculator1 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.

[1]

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4
Sme Calculator1 mark

Shade the subset  A apostrophe intersection B intersection C.

q5a-june-2021-4024-21-cambridge-o-level-maths-d

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5
Sme Calculator2 marks

A school offers piano lessons and flute lessons to a group of 50 children.

Of these children, 28 attend piano lessons

         17 attend flute lessons

         12 attend neither piano lessons nor flute lessons.

By drawing a Venn diagram, or otherwise, find the number of children who attend only the piano lessons.

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1
Sme Calculator2 marks

There are 32 students in a class.

5 do not study any languages.
15 study German (G).
18 study Spanish (S).

cie-igcse-2020-oct-nov-p4-tz1-q9a

Complete the Venn diagram to show this information.

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2a
Sme Calculator3 marks

x is an integer.

ℰ equals open curly brackets x space colon space 41 less or equal than x less or equal than 50 close curly brackets

A equals left curly bracket x space colon space x spaceis an odd numberright curly bracket

B equals left curly bracket x space colon space x spaceis a multiple of 3right curly bracket

C equals left curly bracket x space colon space x spaceis a prime numberright curly bracket

Complete the Venn diagram to show this information.

cie-igcse-2020-may-june-p4-tz1-q5

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2b
Sme Calculator2 marks

List the elements of

i)
A intersection C comma
 
[1]
ii)
open parentheses B union C close parentheses apostrophe.

[1]

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2c
Sme Calculator1 mark

Find straight n open parentheses A intersection B intersection C close parentheses.

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3a
Sme Calculator2 marks

calligraphic E equals{students in a school}
F equals{students who play football}
B equals{students who play baseball}
 
There are 240 students in the school.
 
• 120 students play football
• 40 students play baseball 
• 90 students play football but not baseball.

Complete the Venn diagram to show this information.
 

cie-igcse-2019-may-jun-p4-tz1-q6a

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3b
Sme Calculator1 mark

Find text n  end text left parenthesis F space apostrophe intersection B apostrophe right parenthesis space.

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4
Sme Calculator3 marks

cie-igcse-2019-march-p4-q9a

Use set notation to complete the statements.

i)
d...................A
 
[1]
ii)
left curly bracket f comma space g right curly bracket equals...............................
 
[1]
iii)
Complete the statement.
 

straight n left parenthesis......................... right parenthesis equals 6 [1]

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5
Sme Calculator1 mark

In the Venn diagram below, shade space C intersection D apostrophe.

cie-igcse-2019-march-p4-q9b

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6
Sme Calculator2 marks

The number of members of a leisure centre using the exercise machines (E), the swimming pool (S) and the tennis courts (T) is shown on the Venn diagram.

cie-igcse-2018-may-jun-1-p4-q10c

i)
Find the number of members using only the tennis courts.
 
[1]
ii)
Find the number of members using the swimming pool.


[1]

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1a
Sme Calculator2 marks

q11-paper4-spec-2025-cie-igcse-further-maths

straight n left parenthesis calligraphic E right parenthesis space equals space 20 comma space straight n left parenthesis A space union space B right parenthesis apostrophe space equals space 3 comma space straight n left parenthesis A right parenthesis space equals space 10 space space and space space straight n left parenthesis B right parenthesis space equals space 13.
The Venn diagram shows some of this information.

Find

n(A ∩ B)

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1b
Sme Calculator1 mark

n(A′ ∩ B) .

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2a
Sme Calculator2 marks

cie-igcse-2018-oct-nov-p4-tz1-q6a

 
The Venn diagram above shows information about the number of students who study Music (M), Drama (D) and Geography (G).

i)
How many students study Music?
 
[1]
ii)
How many students study exactly two subjects?
 

[1]

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2b
Sme Calculator1 mark

In the Venn diagram above, shade  M intersection D apostrophe.

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3a
Sme Calculator4 marks

calligraphic E equals left curly bracket x space colon space x spaceis an integer and 1 less or equal than x less or equal than 10 right curly bracket
A equals left curly bracket x space colon space x spaceis evenright curly bracket
4 element of A intersection B straight n left parenthesis A intersection B right parenthesis equals 1 left parenthesis A union B right parenthesis apostrophe equals left curly bracket 1 comma 7 comma 9 right curly bracket
 

cie-igcse-2018-oct-nov-p4-tz1-q6b

Complete the Venn diagram using this information.

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3b
Sme Calculator1 mark

Use your Venn diagram to complete the statement.

B equals left curly bracket....................................................right curly bracket

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4
Sme Calculator1 mark

The number of members of a leisure centre using the exercise machines (E), the swimming pool (S) and the tennis courts (T) is shown on the Venn diagram.

cie-igcse-2018-may-jun-1-p4-q10c

Find straight n left parenthesis T intersection left parenthesis E union S right parenthesis right parenthesis.

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5a
Sme Calculator1 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

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5b
Sme Calculator1 mark

straight n left parenthesis A space intersection space B right parenthesis

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5c
Sme Calculator1 mark

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

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5d
Sme Calculator1 mark

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

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6
Sme Calculator3 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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7
Sme Calculator3 marks

The sets A, B and C are shown in the Venn diagram.

q5b-june-2018-4024-2-cambridge-o-level-maths-d

i)
Find straight n left parenthesis A space union space B right parenthesis.

[1]

ii)
(a)
Given that A intersection B apostrophe intersection C apostrophe equals open curly brackets 2 comma 6 comma 14 comma 18 close curly brackets commalist the members of C.

[1]

(b)
Describe the set C in words.

C = {space x space colon space x space is ........................... } [1]

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1a
Sme Calculator3 marks

This year, 40 students have each travelled by one or more of plane (P), train (T) or boat (B).

7 have travelled only by plane.
11 have travelled only by train.
9 have travelled only by boat.

straight n left parenthesis P intersection T right parenthesis equals 8
straight n left parenthesis B intersection T right parenthesis equals 3
straight n left parenthesis B intersection P right parenthesis equals 6

cie-igcse-2020-march-p4-tz2-q9a

Complete the Venn diagram.

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1b
Sme Calculator1 mark

Find straight n left parenthesis left parenthesis P union B right parenthesis apostrophe right parenthesis.

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1c
Sme Calculator1 mark

Use set notation to complete the statement.


left parenthesis P union T union B right parenthesis apostrophe equals........................... 

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2a
Sme Calculator2 marks
i)
Use set notation to complete this statement.
 

open parentheses G union M union H close parentheses apostrophe equals....................... [1]

ii)
Find space straight n open parentheses G intersection open parentheses M union H close parentheses close parentheses.
 

[1]

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2b
Sme Calculator4 marks

50 students study at least one of the subjects geography (G), mathematics (M) and history (H).
18 study only mathematics.
19 study two or three of these subjects.
23 study geography.
 
The Venn diagram below is to be used to show this information.

cie-igcse-2019-march-p4-q9c

i)
Show that x equals 4.
 
[2]
ii)
Complete the Venn diagram.
 

[2]

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3a
Sme Calculator3 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

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3b
Sme Calculator2 marks

Given that a total of 50 students answered the question,

work out the value of x.

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

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3c
Sme Calculator1 mark

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

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4a
Sme Calculator3 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

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4b
Sme Calculator3 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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5a
Sme Calculator2 marks

A and B are two sets.

n(ξ) = 37

n(A) = 22

n(A ∩ B) = 12

n(A ∪ B) = 30

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

q5a-very-hard-ocr-gcse-maths-extended

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5b
Sme Calculator2 marks

Find

(i)  n(A ∩ B′)

[1]

(ii) n(A′ ∪ B′)

[1]

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6
Sme Calculator6 marks

calligraphic E = { A, C, E, G, H, J, N, R, T, Z }

W = { x space colon space x has rotational symmetry of order 2 }
X = {space x space colon space x space has line symmetry }

Y = { R, A, N, G, E }

i)
Complete the Venn diagram.
[3]
ii)
List the elements of X intersection open parentheses W union Y close parentheses apostrophe.
iii)
Find  straight n open parentheses W union X union Y close parentheses apostrophe.

[1]

iv)
Using set notation, complete this statement. 
................................... = empty set[1] 

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