The document contains examples and exercises on sets and Venn diagrams. It includes questions that ask the reader to: 1) Shade regions in Venn diagrams that represent given sets; 2) Find the number of elements in sets defined within Venn diagrams; 3) List elements that are the intersection or union of given sets; and 4) Draw additional sets in incomplete Venn diagrams based on defined conditions.

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CHAPTER 3: SETS
EXERCISE 2
1. Given P = { 1,4, 6, 8, 9} , Q = { 3,4, 6, 7, 10} , R = { 2, 3,4, 8,9 }
List the elements in the intersection of the following set.
P ∩ Q ∩ R =
ANSWER: ………………….
2 Given ξ = A ∪B ∪ C . Shade the region represented by the set (A ∪ B) ∩ C
ANSWER:
3. Determine the union of the following pairs of sets.
A = { x : x is a factor12 }
B = { x : x is a multiple of 4 less than 16 }
ANSWER: ………………….
4. Given that the universal set ξ = { x : 14 ≤ x ≤ 27 , x are integers }.
Set A = { x : x are even numbers }
Set B = { x : x are perfect square numbers }
Find the complement of the following union of sets A and B.
ANSWER: ………………….
ξ
A B
C

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5. Shade the complement of the set, (A ∪ B ∪C )
ANSWER:
6. Given universal set
ξ = P U Q U R such as
Set ξ = { x : 4 ≤ x ≤ 14 , x are integers }
Set P = { x : x are multiples of 6 }
Set Q = { x : x are odd numbers }
Set P U R = { x : x are multiples of 2 }
and P ⊂ R.
Find n ( P‫י‬ ∩ R ).
ANSWER: ………………….
7. Given ξ = { x: ≤ 2 ≤ x ≤ 10 , x are integers } ,
F = { 4,10 } and
G = { Prime numbers }
List the elements for set ( F ∪ G)‫י‬
ANSWER: ………………….
ξ
A
B
C

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8. The shaded region in the Venn diagram below is
ANSWER: ………………….
9. Given universal set :
ξ = { x : 5 ≤ x ≤ 14, x are integers }
P = { x : x are even numbers }
Q = { x : x are prime numbers }
The elements in set P ∪ Q are
ANSWER: ………………….
10. The diagram shows the universal set ξ , set A and B. The shaded
region in the diagram below is represented by the set
ANSWER: …………………
A B
ξ
A B
C
ξ

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CHAPTER 3: SETS
DIAGNOSTIC TEST
1 Diagram 1 is a Venn diagram which shows the elements of the sets P, Q and R.
If the universal set , ξ = P ∪ Q ∪ R , then set P′ ∪ R′ ∩ Q is
A { 5 , 7 }
B { 2 , 6 }
C { 2 , 3 , 6 }
D { 2 , 3 , 6 , 7 }
2 Diagram 2 represents a class of 40 pupils. Set M = {Pupils who play tennis} and
set R = { Pupils who play badminton} .
ξ
Given that n (M) = 19 , n (M ∩ R ) = 9 and the number of pupils who do not play
either game is 7, find the number of pupils who play badminton.
A 10
B 14
C 23
D 25
• 6
• 1
• 4 • 5
• 7
• 2
• 2
• 3
P
R
Q
M R
DIAGRAM 1
DIAGRAM 2

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3 Given that the universal set ξ = E ∪ F ∪ G , G ⊂ F and E ∩ G ≠ ∅ , the Venn
diagram that represents these relationships is
A ξ B ξ
C ξ D ξ
4 Given that the universal set ξ = {x: 1 ≤ x ≤ 10, x is an integer}, set L ={1,3,5,9},
set M = {x: x is a perfect square} and set N = {x: x is a multiple of 3},
n ( L ∪ M ∩ N ′ ) is
A 0
B 2
C 3
D 8
5 Diagram 3 is a Venn diagram with the universal set ξ = X ∪ Y ∪ Z.
The set X ∪ ( Y ∩ Z ) is represented by the regions
A I , V
B I , II , IV
C I , III, V
D I , II , IV , V
E
F
G
E
G
F
E
F
E
F
G
G
X Y Z
DIAGRAM 3
I
II III IV V

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6. Diagram 4 is a Venn diagram, with the universal set ξ = A ∪ B ∪ C.
Diagram 4
The set A ∩ C , is represented by regions
A. II, IV
B. I, II, IV
C. I, II, III
D. II, III, IV
7. The shaded region represents the set
A. A‫י‬ ∩ B ∩ C
B A‫י‬ ∩ B‫י‬ ∩ C
C. ( A ∩ B )‫י‬ ∩ C
D. A ∪ B ∩ C
A
B
C
III
I II IV
V
A
B
C

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8. Given that the universal set ξ = { x : 1 ≤ x < 20 , x is an integer}
The set
E = { Perfect square numbers less than 30 }
F = { Multiples of 4 less than 20 }
List the element E ∩ F‫י‬
A. { 4,16 }
B { 1, 9 }
C. { 8, 12 }
D. { 1, 4, 8, 9, 12, 16 }
9. Diagram below shows the number of clients in three banks.
Given ξ = A ∪ B ∪ C and n(ξ) = 300.
The number of clients for Bank B is more than those in Bank A
by 40 people. Find the value of Y.
A. 30
B. 40
C. 50
D. 60
30 50 X
30
20
40
Y
A
B
C
ξ

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10.
The Venn diagram shows the number of elements in set P ,Q and R. Given
universal set , E = P U Q U R and n(E) = 40 . Find the value of x.
A. 4
B. 5
C. 6
D. 7
4 2x
x
1
5
3
6
P Q
R

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CHAPTER 3: SETS
EXERCISE 1 (Paper 2)
1. The Venn diagram shows set A, B and C. The universal setξ = C
B
A ∪
∪ . Shade
on separate Venn diagrams in Diagram 1 and Diadram 2, the region that represents each
set given below.
a. A B
∪
DIAGRAM 1
b. B’ C
∩
DIAGRAM 2
2. The Venn diagram shows sets P, Q and R. Shade the region in the Diagram 3 and
Diagram 4 which represents
a. P Q R’
DIAGRAM 3
A
B
C
B
C
P Q
R
A

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b. '
R
Q
P ∩
∪
DIAGRAM 4
3. The Venn diagram shows sets E, F and G. The universal set ξ = G
F
E ∪
∪ . Shade
the region that represent each of the following sets in the Diagram 5, Diagram 6 and
Diagram 7.
a. F’ G
∩
DIAGRAM 5
b. (F '
)
G
∪ E
∩
DIAGRAM 6
c. '
( G
E
F ∩
∪ )
DIAGRAM 7
P
R
Q
E
F
G
E
F
G
E
F
G

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4. The Venn diagram shows the relationship among sets A, B, C andξ . Find the number
of elements in the Diagram 8 and Diagram 9.
a. i) n(A∪B)’
ii) n(A∩B∩C’)
ξ
DIAGRAM 8
b.
ξ
DIAGRAM 9
i) n(A∩C∪B)
ii) n(A’∪B)
B
A
C
.1
.2
.3
.4
.9
.7
.6
.5
.8
.10
B
A
C
.a
.c
.b
.f
.g
.d
.e
.i
.h

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5.
ξ
DIAGRAM 10
The Venn diagram in the Diagram 10 shows the sets M, N and P in the universal setξ .
The number of elements in each set is shown by the number in each region. Find
a. n ( N )
P
∪
b. n ( M )
P
∩
c. n ( N '
)
P
∪
M
N
P
6
3 2
1
5
7

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CHAPTER 3: SETS
EXERCISE 2
1. Given the universal set,
ξ = {x:20≤x≤35, where x are integers},
A= {multiples of 5},
B= {x:x are numbers where one of the digit is 0} and
C= {x:x are numbers where the tens digit > the units digit}.
(a) List the elements of set B and C.
(b) Find n(A∪B).
(c) Find n(A∩C).
2. Given set R = {2,4}, S = {1,2,3,4,5,6} and T = {0, 2, 3, 4, 5, 6, 7, 8, 12}. The
universal set, ξ = R∪S∪T.
(a) Draw a Venn diagram to show the relationship amongst R, S and T.
(b) List the elements of S ∩ T
(c) Find n(R’∩T).
3. Shade the following related region in Diagram 1 and Diagram 2.
(a) P∩Q (b) P'∩Q∩R
P Q P Q
R R
DIAGRAM 1 DIAGRAM 2
4. Given the universal set,
ξ = {x:20≤x≤32, x are integers}
set P = {x:x are multiples of 3},
set Q= {x:x are factors of 100} and
set R= {x:x are numbers where the sum of its digits is 5}.
Find
(a) Set P,
(b) Set Q,
(c) n(Q∩R’).

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5. The Venn diagram below shows set P, Q and R. On Diagram 3 and Diagram 4
provided, shade
(a) P’∩Q∩R’
P Q R
DIAGRAM 3
(b) P∪Q’∪R
P Q
R
DIAGRAM 4

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CHAPTER 3: SETS
DIAGNOSTICS TEST
1. The Venn diagram in the answer space shows sets ξ , P, Q and R.
ξ = P ∪ Q ∪ R.
On the Diagram1 and Diagram 2 in the answer space, shade the set
[ 3 marks]
Answer:
(a) P ∩ Q’
DIAGRAM 1
(b) ( P ∩ Q’) ∪ R
DIAGRAM 2
ξ
ξ
P
Q R
P
Q
R

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2. The Venn diagram in the answer space shows sets J, K and L.
ξ = J ∪ K ∪ L.
On the Diagram 3 and Diagram 4 in the answer space, shade the set
[ 3 marks]
Answer:
(a) ( J ∪ L ) ∩ K
DIAGRAM 3
(b) J ∩ ( K’ ∪ L)
DIAGRAM 4
3. The Venn diagram in the answer space shows sets P, S and R.
On the Diagram 5 and Diagram 6 in the answer space, shade the set
[ 3 marks]
Answer:
(a) P ∩ S’
DIAGRAM 5
J K L
P
S
R
J K L

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(b) ( P ∩ R )’ ∩ S’
DIAGRAM 6
4. The Venn diagram in the answer space shows sets A, B and C.
ξ = A ∪ B ∪ C
On the Diagram 7, Diagram 8 and Diagram 9 in the answer space, shade the
[ 3 marks]
Answer:
(a) set A ∪ B
DIAGRAM 7
(b) Set C ∩ B’
DIAGRAM 8
(c) set ( B ∪ C )’ ∩ A
DIAGRAM
P
S
R
A
B C
A
B C
A
B
C

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5. The incomplete Venn diagram in the Diagram 10 shows sets ξ , J and K.
Set L satisfies the following conditions
L ⊂ ξ
L ∩ J ≠ ∅ and L ∩ K ≠ ∅
L ⊂ J = ∅ and L ⊂ K = ∅
Draw the set L in the Diagram 10 in the answer space.
[ 3 marks]
Answer:
DIAGRAM 10
J K
ξ