Mathematics Form 4 Lesson 16: Set - Chapter 3 Sets Exercise

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Lesson 16: Set

Learning Area:1. Sort given objects into groups

2.Define sets by: i) description ii) using set notation 1 / 5 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:

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December, April, March, May, January, June, July and February. Write the set above by:

a) Description

Solution:

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.

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Lesson 16: Set

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}

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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}

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}

December, April, March, May, January, June, July and February. Write the set above by:

a) Description

Solution:

a) Set of months in a year.

b) B = {December, April, March, May, January, June, July, February}

ACTIVITY SHEET

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Lesson 16: Set

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}

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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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:

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Lesson 17: Elements of a set.

Learning Area: Identify whether a given object is a element of a set and use the symbol ∈ or ∉

2 / 6 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

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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}

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4 / 6 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:

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6 / 6 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)

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Given that _P = {1, 2, 3, 4, 5}. Represent set _P by using a Venn diagram Solution:

If D = {x : 1 ≤ x ≤ 10, x is an odd number}, can you draw a Venn diagram to represent the elements in this set?

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Lesson 18: Sets representations using Venn diagrams.

Learning Area: Represent sets by using Venn diagrams.

2 / 6 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:

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?

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If _M= {states of Malaysia}, can you draw a Venn diagram to represent the number of elements in this set?

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4 / 6 QUESTION 1

Question:

Given that _P = {1, 2, 3, 4, 5}. Represent set _P by using a Venn diagram Solution:

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:

ACTIVITY SHEET

Teacher’s copy

P

• 1

• 5

• 2

• 3

• 4

D

• 1

• 9

• 3

• 5

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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:

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: R

• 30 • 33

• 36 • 39

T

• 30 • 40

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6 / 6 QUESTION 5

Question:

If _M = {states of Malaysia}, can you draw a Venn diagram to represent the number of elements in this set?

Solution:

M

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QUESTION 1

ACTIVITY SHEET

Pupils’ copy

Question:

A is the set of letters in the word “TELECOMUNICATION”. List the elements of set A and state the number of elements.

Solution:

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:

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:

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:

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.

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Lesson 19: Number of elements of a set and an empty set.

Learning Area: 1. List the elements and state the number of elements of a set,

2. Determine whether a set is an empty set. 2 / 5 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:

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:

Determine whether Q is an empty set given that set Q = {x_:x_{is prime number and 11 <}x_{< 20}.}

Solution:

X is the set of common multiples of 2 and 3 which are less than 5. Is set X an empty set?

Solution:

Determine whether T is an empty set given that set T = {x_:x_{is factor of 3 and 1 <}x_{< 10}}

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A is the set of letters in the word “TELECOMUNICATION”. List the elements of set A and state the number of elements.

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

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

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:

M = {January, March, May, July, August, October, December} n(M) = 7

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Lesson 19: Number of elements of a set and an empty set.

Learning Area: 1. List the elements and state the number of elements of a set,

2. Determine whether a set is an empty set. 4 / 5 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.

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.

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:

X is the set of common multiples of 2 and 3 which are less than 5. Is set X an empty set?

Solution: X = { }

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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}

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Lesson 20: Equal sets.

Learning Area: Determine whether two sets are equal.

1 / 6

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.

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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:

S = {x_:x_{is a prime number, 1}≤x≤ 10} T = {x_:x_{is an odd number, 1 ≤}x_{≤ 10}} Are sets S and T equal?

Solution:

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:

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.

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3 / 6 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?

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QUESTION 1

Determine if sets A and B are equal.

Solution:

Determine if sets C and D are equal.

Solution:

Determine if sets E and F are equal.

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5 / 6 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?

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.

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W = {vowels in the word ‘STRAIGHT’} V = {vowels in the word ‘BAIT’}

Are sets W and V equal?

Solution: W = {A, I} V = {A, I} W = V

K = {A, B, O, R, T} L = {A, B, U, R, T} Are sets K and L equal?

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Lesson 21: Subset.

Learning Area: Determine whether a given set is a subset of a specific set and use the symbol ⊂ or_⊄._{1 / 7}

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

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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:

P = {x_:x_{is a prime number, 1}≤x≤ 10} Q = {3, 7}

Is set Q a subset of set P? Solution:

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:

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.

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Learning Area: Determine whether a given set is a subset of a specific set and use the symbol ⊂ or_⊄._{3 / 7} 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:

V = {SECONDARY} U = {DRY}

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Learning Area: Determine whether a given set is a subset of a specific set and use the symbol ⊂ or_⊄._{5 / 7}

Determine if set B is a subset of set A. Solution:

Determine if set D is a subset of set C. Solution:

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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?

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.

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Learning Area: Determine whether a given set is a subset of a specific set and use the symbol ⊂ or_⊄._{7 / 7} 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} Y ⊂ X

V = {SECONDARY} U = {DRY}

Is set U a subset of set V? Solution:

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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:

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?

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Lesson 22: Subsets representations using Venn diagrams.

Learning Area: 1. Represent subsets by using Venn diagrams.

2. List the subsets for specific set. 2 / 4 QUESTION 3

Question:

List all the subsets of set M in the diagram shown below.

Solution:

If R = {x _{: 30}≤x≤ 50, x_{is a multiple of 5 and 10}, can you list all the subsets for this set?} Solution:

If T = {1, 2, 3, 4, 5}, can you list all the subsets of set T which contain three elements?

Solution: M

• 1

• 5

• 3

• 6

• 4

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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:

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:

ACTIVITY SHEET

Teacher’s copy

P

• 1

• 5

• 2

• 3

• 4

A

• 2

• 8

• 4

• 6

• 10

Q

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Lesson 22: Subsets representations using Venn diagrams.

Learning Area: 1. Represent subsets by using Venn diagrams.

2. List the subsets for specific set. 4 / 4 QUESTION 3

Question:

List all the subsets of set M in the diagram shown below.

Solution:

{30, 40} {30, 50} {40, 50}{30,40,50}

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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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:

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Lesson 23: Set, universal set and the compliment of a given set.

Learning Area: 1. Ilustrate the relationship between set and universal set using Venn diagram.

2. Determine the complement of a given set. 2 / 4 QUESTION 3

Question:

Determine the complement of set M in the diagram shown below.

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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 _ = {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:

ACTIVITY SHEET

Teacher’s copy

ξ

• 2

• 7 • 3

• 5 Q

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Lesson 23: Set, universal set and the compliment of a given set.

Learning Area: 1. Ilustrate the relationship between set and universal set using Venn diagram.

2. Determine the complement of a given set. 4 / 4 QUESTION 3

Question:

Determine the complement of set M in the diagram shown below.

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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

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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.

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1) 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 =………

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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 = {………...}

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Lesson 26: The intersection of sets representations and A ∩ B and A and B.

Learning Area: 1. Represent the intersection of sets using Venn diagram.

2. State the relationship between i) A_∩B_{and A, ii)}A_∩B and B_{1 /6} 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:

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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.}

Solution:

A

• 1

• 5 • 3

• 6

• 4 • 2

• 9

• 10 • 7 • 8

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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

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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:

ACTIVITY SHEET

Teacher’s copy

Q

• 2 • 1

• 3

• 4 • 5

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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.}

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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

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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.

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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'_{) = ?}

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Lesson 29: Union of two sets a_{nd three sets.} determine the elements of the union of set E and set F?

Solution:

QUESTION 3

Question:

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QUESTION 4

Question:

If U = {a : 1 ≤a≤ 30, a is a multiple of 6}, V = {b : 1 ≤b≤ 30, b is a multiple of 5 } and

W = {c : 1 ≤a≤ 30, a is a multiple of 4}, can you the determine elements of the union of set U, set V and set W?

Solution:

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?

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Lesson 29: Union of two sets a_{nd three sets.} determine the elements of the union of set E and set F?

Solution:

Given the Venn diagram below, determine the elements of the union of set X and set Y.

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QUESTION 4

Question:

If U = {a : 1 ≤a≤ 30, a is a multiple of 6}, V = {b : 1 ≤b≤ 30, b is a multiple of 5}and

W = {c : 1 ≤a≤ 30, a is a multiple of 4}, can you the elements of the union of set U, set V and set W?

Solution:

U = {4, 8, 12, 16, 20, 24, 28} V = {6, 12, 18, 24, 30} 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:

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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.

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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

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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.

3. Shade the sections on the Venn diagram which match the given statement.

• What is the relation between A ∪ C and A?

Answer:

• What is the relation between (C ∪ B)’ and C’_{∩ B’?}

Answer:

Show A ∪ Con the Venn diagrams. Show (A∪ C) ∩ Aon the Venn diagram.

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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?

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Lesson 32: Problem solving involving union of sets.

Learning Area: 1.Determine the union of: i) two sets ; ii) three sets;

and use the symbol ∪ and ∩ 2 / 4 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.

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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 inA_∪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.

Therefore, n(F_{) = n(}M_{) + n(}S_{) – n(}M_∩S_{) + n(}M_∪S_)’ 35 = 20 + 25 – 15 + n(M_∪S_)’

n(M_∪S_{)’ = 35 – 20 – 25 + 15} = 5

There are 5 pupils that do not like both the subject.

(67)

Lesson 32: Problem solving involving union of sets.

Learning Area: 1.Determine the union of: i) two sets ; ii) three sets;

and use the symbol ∪ and ∩ 4 / 4 QUESTION 3

Question:

Given that Mr Hisham sells news paper to 50 families in Taman Wawasan. Twenty six of these families buy the English dailies, 23 families buy 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:

The number of families in Taman Wawasan that buy news paper [n(N_{)] from Mr Hisham is 50.} The number of families in Taman Wawasan that buy the English dailies [n(E_{)] from Mr Hisham is} 26.

The number of families in Taman Wawasan that buy the Malay dailies [n(M_{)] from Mr Hisham is} 26.

The number of families in Taman Wawasan that buy the neither the dailies [n(O_{)] from Mr Hisham} is 20.

n(E_{) = n(}N_{) + n(}M_{) – n(}N_∩M_{) + n(}N_∪M_)’ 50 = 26 + 23 – n(N_∩M_{) + 20}

n(N_∩M_{) = 69 – 50} = 19.

There are 19 families that buy both the enclish and Malay dailies from Mr Hisham.

QUESTION 4

Question:

Given that the numbers of candidate for the English oral examination in a class is 45. 20 pupils got A, 10 got B and the others got C. Determine the number of pupils that got C using the concept of union of sets. because a pupil can only have one grade therefore all the intersections are empty sets. 45 = 20 + 10 + n(C₎

n(C_{)= 45 – 30} = 15

(68)

Lesson 33

Class: Date:

Instruction:

1. In this activity, you will be given sets with combined operations and asked to draw the representation in a Venn diagram.

3. Draw the sets in a Venn diagram which match the given sets.

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Class Activity

Lesson 34

Class: Date:

Instruction:

In this activity, you will find the corresponding representation of a given phrase using a Venn diagram. 1. Shade the suitable regions in the Venn diagrams, to construct the representation set of the given

phrase.

2. Write the mathematical expression of the phrase.

Phrase:

Pupils in a class studying Math and Science. Show the set of students studying only Math or only Science.

1.

Mathematical expression:

Phrase:

Pupils in a class take Biology, Physics and

Chemistry. All students in the class take at least one of these courses.

Show the set of students taking only one course or taking three of them.

2.