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ANSWER / JAWAPAN
CHAPTER 03 – SETS (MATHEMATICS FORM 4)
BAB 03 – SETS (MATEMATIK TINGKATAN 4)
© HAK CIPTA TERPELIHARA MAY 2013
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1
Latihan Matematik Tingkatan 4
Exercise Mathemtics Form 4
Bab 03 – SETS
Chapter 03 – SETS
JAWAPAN / ANSWER
Question: http://goo.gl/Ny39Z
EXERCISE 2
1. {4}
2. (𝐴 ∪ 𝐵) ∩ 𝐶
3. 𝐴 = {1, 2, 3, 4, 6, 12}
𝐵 = {4, 8, 12}
𝐴 ∪ 𝐵 = {1, 2, 3, 4, 6, 8, 12}
4. 𝐴 = {14, 16, 18, 20, 22, 24, 26}
𝐵 = {16, 25}
𝐴 ∪ 𝐵 = {14, 16, 18, 20, 22, 24, 25, 26} (𝐴 ∪ 𝐵)′ = {15, 17, 19, 21, 23, 27}
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ANSWER / JAWAPAN
CHAPTER 03 – SETS (MATHEMATICS FORM 4)
BAB 03 – SETS (MATEMATIK TINGKATAN 4)
© HAK CIPTA TERPELIHARA MAY 2013
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2
5. (𝐴 ∪ 𝐵 ∪ 𝐶)
6. 𝑃 = {6, 12}
𝑄 = {5, 7, 9, 11, 13}
𝑃 ∪ 𝑅 = {4, 6, 8, 10, 12, 14} 𝑃 ⊂ 𝑅
𝑠𝑜, 𝑅 = {4, 6, 8, 10, 12, 14}
𝑃′ ∩ 𝑅 = {4, 8, 10, 14}
7. 𝐹 = {4, 10}
𝐺 = {2, 5, 7}
𝐹 ∪ 𝐺 = {2, 4, 5, 7, 10} (𝐹 ∪ 𝐺)′ = {3, 6, 8, 9}
8. 𝐴′ ∩ (𝐵 ∪ 𝐶)
9. 𝑃 = {6, 8, 10, 12, 14}
𝑄 = {5, 7, 11, 13} 𝑃 ∪ 𝑄 = {5, 6, 7, 8, 10, 11, 12, 13, 14}
10. 𝐴′ ∩ 𝐵
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ANSWER / JAWAPAN
CHAPTER 03 – SETS (MATHEMATICS FORM 4)
BAB 03 – SETS (MATEMATIK TINGKATAN 4)
© HAK CIPTA TERPELIHARA MAY 2013
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3
DIAGNOSTIC TEST
1. 𝜉 = {1 , 2, 2, 3, 4, 5, 6, 7}
𝑃 = {1, 2, 2, 4, 6}
𝑄 = {2, 3, 5, 6, 7}
𝑅 = {5, 7}
𝑃′ ∪ 𝑅′ ∩ 𝑄 = {2, 3, 6, 7}𝑫
2. 𝑪
3. A/D
4. 𝐿 = {1, 3, 5, 9}
𝑀 = {1, 4, 9}
𝑁 = {3, 6, 9}
𝐿 ∪ 𝑀 ∩ 𝑁′ = {1, 4, 5} 𝑪 = 𝟑 𝒊𝒕𝒆𝒎𝒔
5. 𝑌 ∩ 𝑍 = {𝐼𝑉}
𝑋 = {𝐼, 𝐼𝐼}
𝑋 ∪ (𝑌 ∩ 𝑍) = {𝐼, 𝐼𝐼, 𝐼𝑉} 𝑩
6. [Cancel Question]
7. C
8. 𝐸 = {1, 4, 9, 16}
𝐹 = {4, 8, 12, 16}
𝐸 ∩ 𝐹′ = {1, 9}𝑩
9. 𝐴 = 30 + 50 + 20 + 40 = 140
𝐵 = 𝐴 + 40
= 140 + 40
= 180
180 = 50 + 20 + 30 + 𝑋
= 100 + 𝑋
𝑋 = 180 − 100
= 80
30 + 50 + 20 + 40 + 30 + 𝑋 + 𝑌 = 300
170 + 80 + 𝑌 = 300
𝑌 = 50 𝑪
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ANSWER / JAWAPAN
CHAPTER 03 – SETS (MATHEMATICS FORM 4)
BAB 03 – SETS (MATEMATIK TINGKATAN 4)
© HAK CIPTA TERPELIHARA MAY 2013
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4
10. 4 + 𝑥 + 5 + 1 + 2𝑥 + 3 + 6 = 40
19 + 3𝑥 = 40
3𝑥 = 21
𝑥 = 7 𝑫
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ANSWER / JAWAPAN
CHAPTER 03 – SETS (MATHEMATICS FORM 4)
BAB 03 – SETS (MATEMATIK TINGKATAN 4)
© HAK CIPTA TERPELIHARA MAY 2013
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5
EXERCISE 1 (Paper 2)
1. setξ = A∪ B ∪C
(a) 𝐴 ∪ 𝐵
(b) 𝐵′ ∩ 𝐶
2. 𝜉 = 𝑃 ∪ 𝑄 ∪ 𝑅
(a) 𝑃 ∩ 𝑄 ∪ 𝑅′
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ANSWER / JAWAPAN
CHAPTER 03 – SETS (MATHEMATICS FORM 4)
BAB 03 – SETS (MATEMATIK TINGKATAN 4)
© HAK CIPTA TERPELIHARA MAY 2013
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(b) 𝑃 ∪ 𝑄 ∩ 𝑅′
3. ξ = E ∪ F ∪G
(a) 𝐹′ ∩ 𝐺
(b) (𝐹 ∪ 𝐺)′ ∩ 𝐸
(c) 𝐹 ∪ (𝐸 ∩ 𝐺′)
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ANSWER / JAWAPAN
CHAPTER 03 – SETS (MATHEMATICS FORM 4)
BAB 03 – SETS (MATEMATIK TINGKATAN 4)
© HAK CIPTA TERPELIHARA MAY 2013
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7
4. _
a. 𝜉 = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
𝐴 = {1, 2, 4, 8, 9}
𝐵 = {1, 2, 3, 4, 5}
𝐶 = {4, 5,6, 7, 8}
i) 𝐴 ∪ 𝐵 = {1, 2, 3, 4, 5, 8, 9}
(𝐴 ∪ 𝐵)′ = {6, 7, 10}
𝑛((𝐴 ∪ 𝐵)′) = 3
ii) 𝐶′ = {1, 2, 3, 9, 10}
𝐴 ∩ 𝐵 ∩ 𝐶′ = {1, 2}
𝑛(𝐴 ∩ 𝐵 ∩ 𝐶′) = 2
b. 𝜉 = {𝑎, 𝑏, 𝑐, 𝑑, 𝑒, 𝑓, 𝑔, ℎ, 𝑖}
𝐴 = {𝑎, 𝑏, 𝑐, 𝑓, 𝑔}
𝐵 = {𝑑, 𝑒, 𝑓, 𝑔} 𝐶 = {𝑎}
i) 𝐴 ∩ 𝐶 ∪ 𝐵 = {𝑎, 𝑑, 𝑒, 𝑓, 𝑔}
𝑛(𝐴 ∩ 𝐶 ∪ 𝐵) = 5
ii) 𝐴′ ∪ 𝐵 = {𝑑, 𝑒, 𝑓, 𝑔, ℎ, 𝑖}
𝑛(𝐴′ ∪ 𝐵) = 6
5. 𝑛(𝜉) = 6 + 3 + 2 + 1 + 5 + 7 = 𝟐𝟒
𝑛(𝑀) = 6 + 3 + 2 + 1 = 𝟏𝟐
𝑛(𝑁) = 3 + 2 = 𝟓
𝑛(𝑃) = 1 + 2 + 5 = 𝟖
a. 𝑛(𝑁 ∪ 𝑃) = 3 + 2 + 1 + 5 = 𝟏𝟏
b. 𝑛(𝑀 ∩ 𝑃) = 1 + 2 = 𝟑
c. 𝑛(𝑁 ∪ 𝑃)′ = 𝑛(𝜉) − 𝑛(𝑁 ∪ 𝑃) = 24 − 11 = 𝟏𝟑
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ANSWER / JAWAPAN
CHAPTER 03 – SETS (MATHEMATICS FORM 4)
BAB 03 – SETS (MATEMATIK TINGKATAN 4)
© HAK CIPTA TERPELIHARA MAY 2013
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8
EXERCISE 2
1. 𝜉 = {𝑥: 20 ≤ 𝑥 ≤ 35, 𝑥 𝑎𝑟𝑒 𝑖𝑛𝑡𝑒𝑔𝑒𝑟𝑠}
𝐴 = {20, 25, 30, 35}
𝐵 = {20, 30}
𝐶 = {23, 24, 25, 26, 27, 28, 29, 34, 35}
(a) 𝐵 = {20, 30}
𝐶 = {23, 24, 25, 26, 27, 28, 29, 34, 35}
(b) 𝐴 ∪ 𝐵 = {20, 25, 30, 35}
𝑛(𝐴 ∪ 𝐵) = 4
(c) 𝐴 ∩ 𝐶 = {25, 35}
𝑛(𝐴 ∩ 𝐶) = 2
2. ξ = 𝑅 ∪ 𝑆 ∪ 𝑇
𝑅 = {2, 4}
𝑆 = {1, 2, 3, 4, 5, 6} 𝑇 = {0, 2, 3, 4, 5, 6, 7, 8, 12}
a. _
b. 𝑆 ∩ 𝑇 = {2, 3, 4, 5, 6}
c. 𝑅′ ∩ 𝑇 = {0, 3, 5, 6, 7, 8, 12}
𝑛(𝑅′ ∩ 𝑇) = 7
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ANSWER / JAWAPAN
CHAPTER 03 – SETS (MATHEMATICS FORM 4)
BAB 03 – SETS (MATEMATIK TINGKATAN 4)
© HAK CIPTA TERPELIHARA MAY 2013
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9
3. _
(a) 𝑃 ∩ 𝑄
(b) 𝑃′ ∩ 𝑄 ∩ 𝑅
4. 𝜉 = {𝑥: 20 ≤ 𝑥 ≤ 32}
𝑃 = {21, 24, 27, 30}
𝑄 = {20, 25}
𝑅 = {23, 32}
(a) Set 𝑃 = {21, 24, 27, 30}
(b) Set 𝑄 = {20, 25}
(c) 𝑛(𝑄 ∩ 𝑅′) = 𝑛(20, 25} = 2
5. _
(a) 𝑃′ ∩ 𝑄 ∩ 𝑅′
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ANSWER / JAWAPAN
CHAPTER 03 – SETS (MATHEMATICS FORM 4)
BAB 03 – SETS (MATEMATIK TINGKATAN 4)
© HAK CIPTA TERPELIHARA MAY 2013
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(b) 𝑃 ∪ 𝑄′ ∪ 𝑅
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ANSWER / JAWAPAN
CHAPTER 03 – SETS (MATHEMATICS FORM 4)
BAB 03 – SETS (MATEMATIK TINGKATAN 4)
© HAK CIPTA TERPELIHARA MAY 2013
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11
Diagnostic Test
1. _
(a) 𝑃 ∩ 𝑄′
(b) (𝑃 ∩ 𝑄′) ∪ 𝑅
2. _
(a) (𝐽 ∪ 𝐾) ∩ 𝐿
(b) 𝐽 ∩ (𝐾′ ∩ 𝐿)
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ANSWER / JAWAPAN
CHAPTER 03 – SETS (MATHEMATICS FORM 4)
BAB 03 – SETS (MATEMATIK TINGKATAN 4)
© HAK CIPTA TERPELIHARA MAY 2013
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12
3. _
(a) 𝑃 ∩ 𝑆′
(b) (𝑃 ∩ 𝑅)′ ∩ 𝑆
4. _
(a) 𝐴 ∪ 𝐵
(b) 𝐶 ∩ 𝐵′
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ANSWER / JAWAPAN
CHAPTER 03 – SETS (MATHEMATICS FORM 4)
BAB 03 – SETS (MATEMATIK TINGKATAN 4)
© HAK CIPTA TERPELIHARA MAY 2013
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13
(c) (𝐵 ∪ 𝐶)′ ∩ 𝐴
5. .