Latihan Matematik Tingkatan 4 Exercise Mathemtics Form 4 · PDF filechapter 03 – sets...

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ANSWER / JAWAPAN

CHAPTER 03 – SETS (MATHEMATICS FORM 4)

BAB 03 – SETS (MATEMATIK TINGKATAN 4)

© HAK CIPTA TERPELIHARA MAY 2013


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}



http://goo.gl/Ny39Z


ANSWER / JAWAPAN





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




ANSWER / JAWAPAN





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




ANSWER / JAWAPAN





4

10. 4 + 𝑥 + 5 + 1 + 2𝑥 + 3 + 6 = 40

19 + 3𝑥 = 40

3𝑥 = 21

𝑥 = 7 𝑫




ANSWER / JAWAPAN





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′




ANSWER / JAWAPAN





6

(b) 𝑃 ∪ 𝑄 ∩ 𝑅′

3. ξ = E ∪ F ∪G

(a) 𝐹′ ∩ 𝐺

(b) (𝐹 ∪ 𝐺)′ ∩ 𝐸

(c) 𝐹 ∪ (𝐸 ∩ 𝐺′)




ANSWER / JAWAPAN





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




ANSWER / JAWAPAN





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




ANSWER / JAWAPAN





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′




ANSWER / JAWAPAN





10

(b) 𝑃 ∪ 𝑄′ ∪ 𝑅




ANSWER / JAWAPAN





11

Diagnostic Test

1. _

(a) 𝑃 ∩ 𝑄′

(b) (𝑃 ∩ 𝑄′) ∪ 𝑅

2. _

(a) (𝐽 ∪ 𝐾) ∩ 𝐿

(b) 𝐽 ∩ (𝐾′ ∩ 𝐿)




ANSWER / JAWAPAN





12

3. _

(a) 𝑃 ∩ 𝑆′

(b) (𝑃 ∩ 𝑅)′ ∩ 𝑆

4. _

(a) 𝐴 ∪ 𝐵

(b) 𝐶 ∩ 𝐵′




ANSWER / JAWAPAN





13

(c) (𝐵 ∪ 𝐶)′ ∩ 𝐴

5. .



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