Mathematics Form 4 Lesson 16: Set - Chapter 3 Sets Exercise
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Pupils’ copy QUESTION 1 Question: Sort the given objects into three groups. Dog, eagle, cat, house fly, cow, mosquito, ant, sparrow and kingfisher. Solution: QUESTION 2 Question: The numbers of pupils in each form 4 class in S.M. Taman Puteri are 37, 35, 39, 37, 36, 38 and 35. Write the set above by:
a) Description b) Using set notation. Solution: QUESTION 3 Question: December, April, March, May, January, June, July and February.
Write the set above by:
a) Description b) Using set notation. Solution: QUESTION 4 Question: Use set notation to write the sets given below.
a) Set of even numbers from 10 to 20
b) Set of odd numbers from 20 to 30 c) Set of positive integers that is less than 6. Solution: QUESTION 5 Question: Write the following sets in the form of A = {x : a ≤ x ≤ b, x is a whole number}
a) P = {4, 5, 6, …, 12}
b) Q = {11, 12, 13, …, 20}
c) R = {2, 3, 5, 7, 11, 13}
d) S = {1, 3, 5, …, 13}
e) T = {2, 4, 6, …, 12} Solution:
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Teacher’s copy QUESTION 1 Question: Sort the given objects into three groups.
Dog, eagle, cat, house fly, cow, mosquito, ant, sparrow and kingfisher. Solution:
a) Set of animals = {dog, cat, cow}
b) Set of insects = {house fly, mosquito, ant}
c) Set of birds = {eagle, sparrow, kingfisher} QUESTION 2 Question: The numbers of pupils in each form 4 class in S.M. Taman Puteri are 37, 35, 39, 37, 36, 38 and 35. Write the set above by:
c) Description d) Using set notation. Solution:
a) Set of numbers of pupils in form 4 classes in S.M. Taman Puteri
b) A = {37, 35, 39, 37, 36, 38, 35} QUESTION 3 Question: December, April, March, May, January, June, July and February. Write the set above by:
a) Description b) Using set notation. Solution: a) Set of months in a year.
b) B = {December, April, March, May, January, June, July, February} QUESTION 4 Question: Use set notation to write the sets given below.
a) Set of even numbers from 10 to 20
b) Set of odd numbers from 20 to 30 c) Set of positive integers that is less than 6. Solution:
a) E = {10, 12, 14, 16, 18, 20}
b) O = {21, 23, 25, 27, 29}
c) P = {1, 2, 3, 4, 5} QUESTION 5 Question: Write the following sets in the form of A = {x : a ≤ x ≤ b, x is a whole number}
a) P = {4, 5, 6, …, 12}
b) Q = {11, 12, 13, …, 20}
c) R = {2, 3, 5, 7, 11, 13}
d) S = {1, 3, 5, …, 13}
e) T = {2, 4, 6, …, 12} Solution:
a) P = {x : 4 ≤ x ≤ b12, x is a whole number}
b) Q = {x : 11 ≤ x ≤ 20, x is a whole number}
c) R = {x : 2 ≤ x ≤ 13, x is a prime number}
d) S = {x : 1 ≤ x ≤ 13, x is a odd number}
e) T = {x : 2 ≤ x ≤ 12, x is a even number}
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Learning Area: Identify whether a given object is a element of a set and use the symbol
QUESTION 1 Question: Determine if the sports given are the element of A = {sports competed in the MSSM}
a) Football
b) Basketball
c) Badminton
d) Table tennis
e) Tennis
f) Squash Solution:
Pupils’ copy
QUESTION 2 Question: Determine if the months given are the element of Q = {Months in a year which have 31 days}
a) January
b) February
c) March
d) April
e) May
f) June Solution: QUESTION 3 Question: Determine if the numbers given are the element of Y = {x : 1 ≤ x ≤ 20, x is a multiple of 3} Write the set above by:
a) 1
b) 6
c) 15
d) 17
e) 19
f) 21 Solution:
Learning Area: Identify whether a given object is a element of a set and use the symbol QUESTION 4 Question: Determine if the numbers given are the element of R = {x : −10 ≤ x ≤ 10, x is a positive integer}
a) −10
b) −5
c) 0
d) 5
e) 10 Solution: QUESTION 5 Question: Determine if the statement given below is True or False.
∈
a) R {alphabets of the word ROUGH}
b) 7 ∉ {prime numbers}
c) 0 ∉ {positive integers}
d) Malaysia ∈ {countries in Asean}
e) 20 ∈ {multiple of 4} Solution:
Learning Area: Identify whether a given object is a element of a set and use the symbol
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Teacher’s copy QUESTION 1 Question: Determine if the sports given are the element of A = {sports competed in the MSSM}
a) Football
b) Basketball
c) Badminton
d) Table tennis
e) Tennis
f) Squash Solution: a) Football is an element of set A.
b) Basketball is an element of set A.
c) Badminton is an element of set A.
d) Table tennis is an element of set A.
e) Tennis is an element of set A.
f) Squash is an element of set A.
QUESTION 2 Question: Determine if the months given are the element of Q = {Months in a year which have 31 days}
a) January
b) February
c) March
d) April
e) May
f) June Solution: a) January is an element of set Q.
b) February is not an element of set Q.
c) March is an element of set Q.
d) April is not an element of set Q.
e) May is an element of set Q.
f) June is not an element of set Q.
Learning Area: Identify whether a given object is a element of a set and use the symbol QUESTION 3 Question: Determine if the numbers given are the element of Y = {x : 1 ≤ x ≤ 20, x is a multiple of 3}by using
∈ the symbol or ∉.
a) 1
b) 6
c) 15
d) 17
e) 19
f) 21 Solution:
a) 1 ∉ Y
b) 6 Y
∈
c) 15 Y
∈ ∉
d) 17 Y
∉
e) 19 Y
f) 21 ∉ Y QUESTION 4
Question: Determine if the numbers given are the element of R = {x: −10 ≤ x ≤ 10, x is a positive integer} by using the symbol ∈ or ∉ .
a) −10
b) −5
c) 0
d) 5
e) 10 Solution:
a) −10 ∉ R
∉
b) −5 R
c) 0 ∉ R
d) 5 R
∈
e) 10 R
∈
Learning Area: Identify whether a given object is a element of a set and use the symbol QUESTION 5 Question: Determine if the statement given below is True or False.
a) R ∈ {alphabets of the word ROUGH}
b) 7 ∉ {prime numbers}
c) 0 ∉ {positive integers}
∈
d) Malaysia {countries in Asean}
e) 20 ∈ {multiple of 4} Solution:
a) R ∈ {alphabets of the word ROUGH}(True)
b) 7 ∉ {prime numbers}(False)
c) 0 ∉ {positive integers}(True)
∈
d) Malaysia {countries in Asean}(True)
∈
e) 20 {multiple of 4}(True)
Learning Area: Identify whether a given object is a element of a set and use the symbol
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Pupils’ copy QUESTION 1 Question: Given that P = {1, 2, 3, 4, 5}. Represent set P by using a Venn diagram Solution: QUESTION 2 Question: If D = {x : 1 ≤ x ≤ 10, x is an odd number}, can you draw a Venn diagram to represent the elements in this set? Solution:
QUESTION 3 Question: If R = {x : 30 ≤ x ≤ 40, x is a multiple of 3}, can you draw a Venn diagram to represent the elements in this set? Solution: QUESTION 4 Question: If T = {x : 30 ≤ x ≤ 50, x is a multiple of 5 and 10}, can you draw a Venn diagram to represent the elements in this set? Solution:
QUESTION 5 Question: If M = {states of Malaysia}, can you draw a Venn diagram to represent the number of elements in this set? Solution:
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Teacher’s copy QUESTION 1 Question: Given that P = {1, 2, 3, 4, 5}. Represent set P by using a Venn diagram Solution:
P
- 1 •
2
- 3
- 5 4 •
QUESTION 2 Question: If D = {x : 1 ≤ x ≤ 10, x is an odd number}, can you draw a Venn diagram to represent the elements in this set? Solution:
D
1
3
- 5 •
9
- 7
R
- 30 •
33 36 •
- 39
QUESTION 4 Question: If T = {x : 30 ≤ x ≤ 50, x is a multiple of 5 and 10}, can you draw a Venn diagram to represent the elements in this set? Solution:
T
30
40
50
M
14
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Pupils’ copy QUESTION 1 Question: A is the set of letters in the word “TELECOMUNICATION”. List the elements of set A and state the number of elements.
Solution: QUESTION 2 Question: S is the set of multiples of 4 less than 20 that can be divided by 11. List the elements of number of set S. How many elements in it? Solution: QUESTION 3 Question: Given that Y is the Number of elements of a set and empty set of letters in the word “ACTIVITIES”.
(a) List the elements of set Y. (a) State the number of elements of set Y.
Solution: QUESTION 4 Question: M is the set of the months in a year with 31 days. List the elements of set M and state the number of its elements. Solution: QUESTION 5 Question: Given that set A is the set of prime numbers that are less than 0. Determine whether Number of elements of a set and empty set A is an empty set. Solution: QUESTION 6 Question: Given that set B is the set of the factors of 12. Determine whether Number of elements of a set and empty set B is an empty set.
Solution: QUESTION 7 Question: Given that set D is the set of even numbers less than 10. Determine whether number of elements of a set and empty set D is an empty set. Solution: QUESTION 8 Question: Determine whether Q is an empty set given that set Q = {x: x is prime number and 11 < x < 20}. Solution: QUESTION 9 Question: X is the set of common multiples of 2 and 3 which are less than 5. Is set X an empty set? Solution: QUESTION 10 Question: Determine whether T is an empty set given that set T = {x: x is factor of 3 and 1 < x < 10} Solution:
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Teacher’s copy QUESTION 1 Question: is the set of letters in the word “TELECOMUNICATION”. List the elements of set A and state the A number of elements.
Solution: A = {T, E, L, C, O, M, U, N, I, A, T,} n(A) = 11
QUESTION 2 Question: S is the set of multiples of 4 less than 20 that can be divided by 11. List the elements set S. How many elements in it? Solution: S = {} n(S) = 0 QUESTION 3 Question: Given that Y is the Number of elements of a set and empty set of letters in the word “ACTIVITIES”.
(b) List the elements of set Y. (b) State the number of elements of set Y.
Solution: Y = {A, C, T, I, V, E, S} n(Y) = 7
QUESTION 4 Question: is the set of the months in a year with 31 days. List the elements of set M and state the number of M its elements.
Solution: M = {January, March, May, July, August, October, December} n(M) = 7
QUESTION 5 Question: Given that set A is the set of prime numbers that are less than 0. Determine whether Number of elements of a set and empty set A is an empty set.
Solution: A = { } Set A is an empty set.
QUESTION 6 Question: Given that set B is the set of the factors of 12. Determine whether Number of elements of a set and empty set B is an empty set.
Solution: B = {1, 2, 3, 4, 6, 12} Set B is no an empty set.
QUESTION 7 Question: Given that set D is the set of even numbers less than 10. Determine whether Number of elements of a set and empty set D is an empty set.
Solution: D = {2, 4, 6, 8} Set D is not an empty set.
QUESTION 8 Question: Determine whether Q is an empty set given that set Q = {x: x is prime number and 11 < x < 20}.
Solution: Q = {13, 17, 19} Set Q is not an empty set.
QUESTION 9 Question: X is the set of common multiples of 2 and 3 which are less than 5. Is set X an empty set? Solution: X = { } Set X is an empty set.
QUESTION 10 Question: Determine whether T is an empty set given that set T = {x: x is factor of 3 and 1 < x < 10} Solution: T = {3} Set T is not an empty set.
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Pupils’ copy QUESTION 1 Question: A = { , , , }
= { , , , } B Determine if sets A and B are equal.
Solution: QUESTION 2 Question: C = { , , , } D = { , , , } Determine if sets C and D are equal. Solution: QUESTION 3 Question:
= { , , , } E F = { , , , } Determine if sets E and F are equal.
Solution: QUESTION 4 Question: P = {x : x is an odd number, 11 ≤ x ≤ 20}
= {11, 13, 15, 17, 19} Q Are sets P and Q equal? Solution: . QUESTION 5 Question: X = {multiples of 2 which are between 10 and 20} Y = {Even numbers between 10 and 20} Are sets X and Y equal? Solution: QUESTION 6 Question:
= {x : x is a prime number, 1 ≤ x ≤ 10} S
= {x : x is an odd number, 1 ≤ x ≤ 10} T Are sets S and T equal? Solution: QUESTION 7 Question: V = {x : x is a prime number, 11 ≤ x ≤ 20}
= {11, 13, 17, 19} U Are sets V and U equal? Solution: QUESTION 8 Question: Determine whether sets G and H are equal if set G is equal to common factors of 2 while H is even numbers which are less than 10.
Solution:
QUESTION 9 Question: W = {vowels in the word ‘STRAIGHT’} V = {vowels in the word ‘BAIT’} Are sets W and V equal? Solution: QUESTION 10 Question: K = {A, B, O, R, T} L = {A, B, U, R, T} Are sets K and L equal? Solution:
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Teacher’s copy QUESTION 1 Question:
= { , , , } A
= { , , , } B Determine if sets A and B are equal.
Solution: A = B QUESTION 2 Question: C = { , , , } D = { , , , } Determine if sets C and D are equal.
Solution: C ≠ D QUESTION 3 Question: E = { , , , } F = { , , , } Determine if sets E and F are equal.
Solution: E = F QUESTION 4 Question: P = {x : x is an odd number, 11 ≤ x ≤ 20} Q = {11, 13, 15, 17, 19} Are sets P and Q equal? Solution:
= {11, 13, 15, 17, 19} P Q = {11, 13, 15, 17, 19} P = Q
QUESTION 5 Question: X = {multiples of 2 which are between 10 and 20} Y = {Even numbers between 10 and 20} Are sets X and Y equal? Solution: X = {12, 14, 16, 18} Y = {12, 14, 16, 18}
= Y
X QUESTION 6 Question: S = {x : x is a prime number, 1 ≤ x ≤ 10}
= {x : x is an odd number, 1 ≤ x ≤ 10} T Are sets S and T equal? Solution: S = {2, 3, 5, 7} T = {1, 3, 5, 7, 9} S ≠ T QUESTION 7 Question: V = {x : x is a prime number, 11 ≤ x ≤ 20} U = {11, 13, 17, 19} Are sets V and U equal? Solution:
= {11, 13, 17, 19}
V U = {11, 13, 17, 19} V = W QUESTION 8 Question: Determine whether sets G and H are equal if set G is equal to common factors of 2 while H is even numbers which are less than 10.
Solution: G = {1, 2}
= {2, 4, 6, 8} H
≠ H G QUESTION 9 Question: W = {vowels in the word ‘STRAIGHT’} V = {vowels in the word ‘BAIT’} Are sets W and V equal? Solution: W = {A, I}
= {A, I}
V W = V QUESTION 10 Question:
= {A, B, O, R, T} K L = {A, B, U, R, T} Are sets K and L equal? Solution: K≠ L
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Pupils’ copy QUESTION 1 Question: A = { , , , }
= { , , } B Determine if set B is a subset of set A.
Solution: QUESTION 2 Question: C = { , , , } D = { , , , } Determine if set D is a subset of set C. Solution: QUESTION 3 Question:
= { , , , } E F = { , , , } Determine if set F is a subset of set E QUESTION 4 Question: S = {a : a is an odd number, 1 ≤ a ≤ 10}
= {1,5, 7} T Is set T a subset of set S? Solution: . QUESTION 5 Question: G = {multiples of 5 which are between 10 and 30} H = {Even numbers between 10 and 20} Is set H a subset of set G? Solution: QUESTION 6 Question:
= {x : x is a prime number, 1 ≤ x ≤ 10} P
= {3, 7} Q Is set Q a subset of set P? Solution: QUESTION 7 Question: M = {x : x is a prime number, 11 ≤ x ≤ 20}
= {11, 13, 17} N Is set N a subset of set M? Solution: QUESTION 8 Question: Determine whether set R is a subset of set S if set R is equal to common factors of 2 while set S is even numbers which are less than 10.
Solution:
QUESTION 9 Question: X = {vowels in the word ‘TROUGH’} Y = {vowels in the word ‘TOUGH’} Is set Y a subset of set X? Solution: QUESTION 10 Question:
= {SECONDARY}
V = {DRY}
U Is set U a subset of set V? Solution:
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Teacher’s copy QUESTION 1 Question: A = { , , , } B = { , , } Determine if set B is a subset of set A.
Solution: B ⊂ A QUESTION 2 Question: C = { , , , } D = { , , , } Determine if set D is a subset of set C.
Solution: ⊄ C
D QUESTION 3 Question: E = { , , , } F = { , , , } Determine if set F is a subset of set E Solution: F ⊂ E QUESTION 4 Question: S = {a : a is an odd number, 1 ≤ a ≤ 10} T = {1,5, 7} Is set T a subset of set S? Solution: S = {1, 3, 5, 7, 9} T = {1, 5, 7} T ⊂ S
QUESTION 5 Question: G = {multiples of 5 which are between 10 and 30} H = {Even numbers between 10 and 20} Is set H a subset of set G? Solution: G = {15, 20 25} H = {12, 14, 16, 18}
⊄ G H QUESTION 6 Question: P = {x : x is a prime number, 1 ≤ x ≤ 10} Q = {3, 7} Is set Q a subset of set P? Solution: P = {2, 3, 5, 7} Q = {3, 7} Q ⊂ P QUESTION 7 Question: M = {x : x is a prime number, 11 ≤ x ≤ 20} N = {11, 13, 17} Is set N a subset of set M? Solution: M = {11, 13, 17, 19} N = {11, 13, 17} N ⊂ M QUESTION 8 Question: Determine whether set R is a subset of set S if set R is equal to common factors of 2 while set S is even numbers, which are less than 10.
Solution: R = {1, 2} S = {2, 4, 6, 8} R ⊄ S
QUESTION 9 Question: X = {vowels in the word ‘TROUGH’} Y = {vowels in the word ‘TOUGH’} Is set Y a subset of set X? Solution: X = {O, U} Y = {O, U}
⊂ X Y QUESTION 10 Question: V = {SECONDARY} U = {DRY} Is set U a subset of set V? Solution: U ⊂
V
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Pupils’ copy QUESTION 1 Question: Given that P = {1, 2, 3, 4, 5} and Q = {1, 3, 5}. Show the relationship between sets P and Q using a Venn diagram Solution: QUESTION 2 Question: If A = {x : 1 ≤ x ≤ 10, x is an even number} and B = {2, 4, 6}, can you draw a Venn diagram to represent the relationship between these two sets? Solution:
QUESTION 3 Question: List all the subsets of set M in the diagram shown below.
M
- 1 •
6 2 •
3
5
- 4
Solution: QUESTION 4 Question: If R = {x : 30 ≤ x ≤ 50, x is a multiple of 5 and 10}, can you list all the subsets for this set? Solution: QUESTION 5 Question: If T = {1, 2, 3, 4, 5}, can you list all the subsets of set T which contain three elements? Solution:
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Teacher’s copy QUESTION 1 Question: Given that P = {1, 2, 3, 4, 5} and Q = {1, 3, 5}. Show the relationship between sets P and Q using a Venn diagram Solution:
- 2
P Q
- 1 5 •
3 • 4 • QUESTION 2 Question: If A = {x : 1 ≤ x ≤ 10, x is an even number} and B = {2, 4, 6}, can you draw a Venn diagram to represent the relationship between these two sets? Solution:
A B 4 •
- 6
2
- 8 >10
M
- 1 2 • 3 • 4 •
Solution: M = {1, 2, 3, 4} The subsets of set M are: { } {1} {2} {3} {4} {1, 2} {1, 3} {1, 4} {2, 3} {2, 4} {3, 4} {1, 2, 3} {1, 2, 4} {2, 3, 4} {1, 3, 4}{1,2,3,4} QUESTION 4 Question: If R = {x : 30 ≤ x ≤ 50, x is a multiple of 5 and 10}, can you list all the subsets for this set? Solution: R = {30, 40, 50} The subsets of set R are: { } {30} {40} {50} {30, 40} {30, 50} {40, 50}{30,40,50} QUESTION 5 Question: If T = {1, 2, 3, 4, 5}, can you list all the subsets of set T which contain three elements? Solution: The subsets of set T which contain three elements are: {1, 2, 3} {1, 2, 4} {1, 2, 5} {2, 3, 4} {2, 3, 5} {3, 4, 5} {1, 3, 4} {1, 3, 5} {1, 4, 5} {2, 4, 5}
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Pupils’ copy QUESTION 1 Question: Given that ξ = {pupils of S.M. Puteri} and Q = {male pupils of S.M. Puteri}. Show the relationship between sets ξ and Q using a Venn diagram Solution: QUESTION 2 Question: If ξ = {x : 1 ≤ x ≤ 10, x is a prime number} and B = {2, 3}, can you draw a Venn diagram to represent the relationship between these two sets? Solution:
Learning Area: 1. Ilustrate the relationship between set and universal set using Venn QUESTION 3 Question: Determine the complement of set M in the diagram shown below.
ξ
- 9
M
- 7 1 •
6 •
- 2
3 • 5 • 4 •
8
10 Solution: QUESTION 4 Question: If ξ = {x : 1 ≤ x ≤ 10, x is a multiple of 2} and A = {4, 6}, can you determine the complement of set
? A Solution: QUESTION 5 Question: If ξ = {A, B, C, D, E, F} and R = {D, E, F}, can you determine the complement of set R? Solution:
Learning Area: 1. Ilustrate the relationship between set and universal set using Venn
ACTIVITY SHEET
Teacher’s copy QUESTION 1 Question: Given that ξ = {pupils of S.M. Puteri} and Q = {male pupils of S.M. Puteri}. Show the relationship between sets ξ and Q using a Venn diagram Solution:
ξ Q QUESTION 2
Question: If _ = {x : 1 ≤ x ≤ 10, x is a prime number} and B = {2, 3}, can you draw a Venn diagram to represent the relationship between these two sets? Solution:
ξ 1 • B 2 •
3
- 7 •
5
- Learning Area: 1. Ilustrate the relationship between set and universal set using Venn
ξ
9
- M
7
- 1
6
- 2 •
3 • •
5
4
- 8
10
- Solution: M ‘= {7, 8, 9, 10} QUESTION 4 Question: If ξ = {x : 1 ≤ x ≤ 10, x is a multiple of 2} and A = {4, 6}, can you determine the complement of set
A ? Solution: ξ = {2, 4, 6, 8, 10} A = {4, 6} A’ = {2, 8, 10} QUESTION 5 Question: If ξ = {A, B, C, D, E, F} and R = {D, E, F}, can you determine the complement of set R? Solution: R’ = {A, B, C}
Learning Area: 1. Ilustrate the relationship between set and universal set using Venn
Class Activity 1 Lesson: Class: Date: Instructions: 1. In this activity, there are two doors with two different Venn diagrams on them.
2. First, choose one of the Venn diagrams.
3. Then, cut the elements of the sets by using a pair of scissors.
4. Decide on the place where you should stick the elements.
5. Take the statement sheet after you have done the placement correctly.
6. Mark “T” if you think that the statement is true 7. Mark “F” if you think that the statement is false.
{ } { }
17
? _
_ _ _
_ _ _ _
X W _ _
T F T F T F T F
X X W
X W W
′ ⊂
⊂ ′ ′ ⊂
ξ ξ ⊂ ′
11 SHEET 3
15
19
44 , 41 , 37 , 35 ,
22
25
33
35
37
41
44
ξ W SHEET 2
11 = =
17 , 15 ,
33 , 25 , 22 , 19 ,
17 , 15 , 11 44 ,
33 , 25 , 22 , 19 ,
_
Lesson: Class: Date: Instruction:
1. In this activity, there are two types of problems, a problem with 2 sets and a problem with 3 sets.
2. First, choose one of the problem types.
3. Then, write the sets based on your problem type.
4. Determine whether they have any elements in common.
5. Finally write the intersection of these sets based on the common elements of the sets.
1) What is the intersection of set A and set B?
A = {………………………………………………}
B = {………………………………………...........}
A∩B =……………………………………………
2) What is the intersection of set A and set B?
A = {………………………………………………}
B = {………………………………………...........}
A∩B =……………………………………………
3) What is the intersection of set A and set B?
A = {………………………………………………}
B = {………………………………………...........}
A∩B =……………………………………………
4) What is the intersection of set A and set B?
A = {………………………………………………}
B = {………………………………………...........}
A∩B =……………………………………………
5) What is the intersection of set A and set B? A = {………………………………………………} B = {………………………………………...........}
A∩B =……………………………………………
6) What is the intersection of set A and set B?
A = {………………………………………………}
B = {………………………………………...........}
A∩B =……………………………………………
7) What is the intersection of set A and set B?
A = {………………………………………………}
B = {………………………………………...........}
A∩B =……………………………………………
1)What is the intersection of set A, set B and set C?
A = {………………………………………………} B = {………………………………………...........} C = {………………………………………...........} A ∩ B ∩ C =………………………………………
2)What is the intersection of set A, set B and set C?
A = {………………………………………………} B = {………………………………………...........} C = {………………………………………...........} A ∩ B ∩ C =………………………………………
3)What is the intersection of set A, set B and set C ?
A = {………………………………………………} B = {………………………………………...........} C = {………………………………………...........} A ∩ B ∩ C =………………………………………
4)What is the intersection of set A , set B and set C?
A = {………………………………………………} B = {………………………………………...........} C = {………………………………………...........} A ∩ B ∩ C =………………………………………
5)What is the intersection of set A , set B and set C?
A = {………………………………………………} B = {………………………………………...........} C = {………………………………………...........} A ∩ B ∩ C =………………………………………
6)What is the intersection of set A , set B and set C?
A = {………………………………………………} B = {………………………………………...........} C = {………………………………………...........} A ∩ B ∩ C =………………………………………
ACTIVITY SHEET
Pupils’ copy QUESTION 1 Question: Given that A = {1, 2, 3, 4, 5} and B = {4, 5, 6, 7, 8}. Show the relationship between sets A and B using a Venn diagram Solution:
QUESTION 2 Question: If P = {x : 20 ≤ x ≤ 50, x is a multiple of 10} and Q = {10, 20, 30}, can you represent the intersection of the two sets using a Venn diagram? Solution: QUESTION 3 Question: Given the Venn diagram below, determine the relationship between A ∩ B and A.
A B 1 •
9
- 8 •
- 2
7
6
- 3
5 •
- 4
- 10
Solution:
QUESTION 4 Question: If R = {x : 1 ≤ x ≤ 10, x is a prime number} and S = {2, 3, 7}, can you represent the intersection of the two sets using a Venn diagram? Solution: QUESTION 5 Question: Given that C = {a, b, c, x, y, z} and D = {x, y, z}. Show the relationship between sets A and B using a Venn diagram Solution:
ACTIVITY SHEET
Teacher’s copy QUESTION 1 Question: Given that A = {1, 2, 3, 4, 5} and B = {4, 5, 6, 7, 8}. Show the relationship between sets A and B using a Venn diagram Solution:
Q
2 • 6 •
4
- 1 •
7 •
3 • •
5 8 • QUESTION 2 Question: If P = {x : 20 ≤ x ≤ 50, x is a multiple of 10} and Q = {10, 20, 30}, can you represent the intersection of the two sets using a Venn diagram? Solution:
Q
P
20
50 10 • 30 • 40 •
QUESTION 3 Question: Given the Venn diagram below, determine the relationship between A∩B and A.
A B 1 •
9
8
- 2
7 • 6 •
3 • •
5
- 4 10 •
Solution: The relationship between A∩B and A is A∩B is a subset of set A.
QUESTION 4 Question: If R = {x : 1 ≤ x ≤ 10, x is a prime number} and S = {2, 3, 7}, can you represent the intersection of the two sets using a Venn diagram? Solution:
R S
- 1 •
2
- 5 3 •
7
- QUESTION 5 Question: Given that C = {a, b, c, x, y, z} and D = {x, y, z}. Show the relationship between sets A and B using a Venn diagram Solution:
D C x
- D c C
- a x
- c >a <>z
- b Or &bul>z
- b
Class Activity Lesson: 27 Instructions: 1. In this activity, there are 4 questions related with sets.
2. Begin with one of the questions.
3. Then, find the elements of the complement of the intersection of sets.
(M ∩ N ∩ Q)’ = ? (M ∩ N)’ = ? (N ∩ Q)’ = ? (M ∩ Q)’ = ?
M N Q _ a _
2 _ f _ h
_
1 _
7 _ c _
6 _ z _9
_ g
ξ
Class Activity Lesson: 28 Instructions: 1. In this activity, there are 5 questions related with the same givens in the activity.
2. Try to answer each question and write your answers into the boxes.
W : Set of applicants good at MS Word
E :
Set of applicants good at MS Excel
P :
Set of applicants good at MS PowerPoint
P ⊂ W n
(P) = 10 n (W ∩ E) = 6 n (E′) = 16 n ( ξ ) = 29
1. What could be the maximum value of n(W ∩ E ∩ P)?
2. If n(W ∩ E ∩ P) = 2, then n(E) = ?
3. Can W ∩ E ∩ P be an empty set? 4. n(P') = ?
5. Is n(E ∩ P) equal to n(W ∩ E ∩ P)?
ACTIVITY SHEET
Pupil’s copy QUESTION 1 Question: Given that A = {1, 2, 3, 4, 5} and B = {4, 5, 6, 7, 8}. Can you determine the elements of the union of set A and set B? QUESTION 2 Question: If E = {x : 1 ≤ x ≤ 20, x is a prime number} and F = { y : 1 ≤ y ≤ 20, y is an odd number }, can you determine the elements of the union of set E and set F? Solution: QUESTION 3 Question: Given the Venn diagram below, determine the elements of the union of set X and set Y.
Χ Υ Υ
X a
- Υ
- p h >s
- f k
- Solution:
ACTIVITY SHEET
Teacher’s copy QUESTION 1 Question: Given that A = {1, 2, 3, 4, 5} and B = {4, 5, 6, 7, 8}. Can you determine the elements of the union of set A and set B? Solution: A∪B = {1, 2, 3, 4, 5, 6, 7, 8} QUESTION 2 Question: If E = {x : 1 ≤ x ≤ 20, x is a prime number} and F = { y : 1 ≤ y ≤ 20, y is an odd number }, can you determine the elements of the union of set E and set F? Solution: E = {1, 2, 3, 5, 7, 11, 13, 17, 19}
= {1, 3, 5, 7, 9, 11, 13, 15, 17, 19} F E∪F = {1, 2, 3, 5, 7, 9, 11, 13, 15, 17, 19} QUESTION 3 Question: Given the Venn diagram below, determine the elements of the union of set X and set Y.
Χ Υ
X Y
- a <>h <>j • m
- f
- k Solution: The relationship between AB and A is AB is a subset of set A.
= {6, 12, 18, 24, 30}
V W = {5, 10, 15, 20, 25, 30} U∪V∪W = {4, 5, 6, 8, 10, 12, 15, 16, 18, 20, 24, 25, 28, 30} QUESTION 5 Question: Given that P = {a, b, c}, Q = {1, 2, 3} and R = {x, y, z}. Determine the elements of the union of set P, set Q and set R? Solution: P∪Q∪R = {a, b, c, 1, 2, 3, x, y, z}
Class Activity 1 Lesson 30 Class: Date:
Instruction:
1. In this activity, you will be given a Venn diagram containing three sets and some statements regarding the sets.
2. Read the statement carefully.
3. Shade the sections on the Venn diagram which match the given statement. Show A ∪ B ∪ C on the Venn diagram.
Show A ∪ B ∪ C on the Venn diagram. Question 3 Show A ∪ B ∪ C on the Venn diagram.
Question 4 Show A ∪ B ∪ C on the Venn diagram. Class Activity 1 Lesson: Class: Date: Instruction:
1. In this activity, you will be given a Venn diagram containing three sets and some statements regarding the sets.
2. Read the statement carefully.
3. Shade the sections on the Venn diagram which match the given statement.
Show A ∪ C on the Venn diagrams. Show (A ∪ C) ∩ A on the Venn diagram.
Show (C ∪ B)’ on the Venn diagram. Show C’ ∩ B’ on the Venn diagram.
- What is the relation between A ∪ C and A? Answer:
- What is the relation between (C ∪ B)’ and C’ ∩ B’?
ACTIVITY SHEET
Pupils’ copy QUESTION 1 Question: In a class, there are 16 pupils play chess and 25 pupils play monopoly. Given that there are only 10 pupils plays both games, how many pupils are there in the class? Solution: QUESTION 2 Question: In a class of 35 pupils, 20 of them enjoy Mathematics, 25 of them enjoy Science. If 15 of the pupils in that class enjoy both Mathematics and Science, how many pupils of that class do not enjoy both subjects? Solution:
QUESTION 3 Question: Given that Mr Hisham sells newspaper to 50 families in Taman Wawasan. Twenty six of these families buy the English dailies, 23 buys the Malay dailies while 20 of them do not buy either the English or Malay dailies. Determine the number of families that buy both the English and Malay dailies.
Solution: QUESTION 4 Question: Given that the numbers of candidate for the English oral examination in a class is 45. 20 pupils scored A, 10 pupils scored B and the others scored C. Determine the number of pupils that scored C, using the concept of union of sets. Solution:
ACTIVITY SHEET
Teacher’s copy QUESTION 1 Question: In a class, there are 16 pupils play chess and 25 pupils play monopoly. Given that there are only 10 pupils plays both games, how many pupils are there in the class? Solution: The number of pupils in the class is equal to the number of elements in A∪B. n(A∪B) = n(A) + n(B) – n(A∩B) = 16 + 25 – 10 = 31 QUESTION 2 Question: In a class of 35 pupils, 20 of them enjoy Mathematics, 25 of them enjoy Science. If 15 of the pupils in that class enjoy both Mathematics and Science, how many pupils of that class do not enjoy both subjects? Solution: Let F be the set of pupils in the class, M be the set of pupils that likes Mathematics, S be the set of pupils that likes Science.