The document provides examples and exercises on sets and Venn diagrams. It includes 10 questions with diagrams where students are asked to: 1) Shade regions in Venn diagrams that represent given sets based on set relationships 2) Find the number of elements in regions of Venn diagrams 3) Draw and complete Venn diagrams based on given set relationships and 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:
ξ
A B
C
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: ………………….
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5. Shade the complement of the set, (A ∪ B ∪C )
ANSWER:
A
ξ
B
C
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 ( P‫ ∩ י‬R ).
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: ………………….
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8. The shaded region in the Venn diagram below is
ξ
A B
C
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
ξ
A B
ANSWER: …………………
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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.
P Q
•1 R
•2 •3
•7
•4 •6 •5
•2
DIAGRAM 1
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
M R
DIAGRAM 2
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
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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 F B ξ
E G
E
G F
C ξ D ξ
G F
E E
F G
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.
X Y Z
I
II III IV V
DIAGRAM 3
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
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6. Diagram 4 is a Venn diagram, with the universal set ξ = A ∪ B ∪ C.
A
B
I II IV
V
III
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
B
C
A. A‫ ∩ י‬B ∩ C
B A‫ ∩ י‬B‫ ∩ י‬C
C. ( A ∩ B )‫ ∩ י‬C
D. 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.
ξ
A
B
30 50 X
20
40
30
Y
C
A. 30
B. 40
C. 50
D. 60
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10.
P Q
4 x 2x
5
1 3
6
R
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
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CHAPTER 3: SETS
EXERCISE 1 (Paper 2)
1. The Venn diagram shows set A, B and C. The universal set ξ = A ∪ B ∪ C . Shade
on separate Venn diagrams in Diagram 1 and Diadram 2, the region that represents each
set given below.
a. A∪ B
A
C
B
DIAGRAM 1
b. B’ ∩ C
A
C
B
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’
P Q
R
DIAGRAM 3
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P
b. P ∪ Q ∩ R '
Q
R
DIAGRAM 4
3. The Venn diagram shows sets E, F and G. The universal set ξ = E ∪ F ∪ G . Shade
the region that represent each of the following sets in the Diagram 5, Diagram 6 and
Diagram 7.
a. F’ ∩ G
E
G F
DIAGRAM 5
b. (F ∪ G ) ' ∩ E
E
G F
DIAGRAM 6
c. F ∪ (E ∩ G ' )
E
G
F DIAGRAM 7
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4. The Venn diagram shows the relationship among sets A, B, C and ξ . Find the number
of elements in the Diagram 8 and Diagram 9.
a. i) n(A∪B)’
ii) n(A∩B∩C’)
ξ
.3
A .1 B
.9 .2 .4 .5 .10
.8
.7
.6
C
DIAGRAM 8
b.
ξ
.c A .i
B
.d .f
.g .a
C
.e .b
.h
DIAGRAM 9
i) n(A∩C∪B)
ii) n(A’∪B)
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5.
ξ
M
6
P
1
N 3 2
5
7
DIAGRAM 10
The Venn diagram in the Diagram 10 shows the sets M, N and P in the universal set ξ .
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) '
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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’
ξ
P
Q R
DIAGRAM 1
(b) ( P ∩ Q’) ∪ R
ξ
P
Q
R
DIAGRAM 2
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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
J K L
DIAGRAM 3
(b) J ∩ ( K’ ∪ L)
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’
P R
S
DIAGRAM 5
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(b) ( P ∩ R )’ ∩ S’
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
A
B C
DIAGRAM 7
(b) Set C ∩ B’
A
B C
DIAGRAM 8
(c) set ( B ∪ C )’ ∩ A
A
B
C
DIAGRAM
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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:
ξ
J K
DIAGRAM 10
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