Module5 sets-090823035141-phpapp02
2 likes276 views
This document contains a summary of a maths tuition module on sets. It includes 8 questions covering topics like Venn diagrams, set operations, and calculating cardinalities. The questions involve tasks like shading regions in Venn diagrams, listing set elements, and finding unions, intersections and complements of sets. The document also provides the full answers to each question in the form of diagrams and numeric expressions.
![PPR Maths nbk
MODUL 5
SKIM TUISYEN FELDA (STF) MATEMATIK SPM “ENRICHMENT”
TOPIC : SETS
MASA : 1 JAM
1. The Venn diagram in the answer space shows the universal set ξ, sets P, Q and
R.
The universal set ξ = P ∪ Q ∪ R.
On the diagram in the answer space, shade the region for
(a) P ∩ Q,
(b) P ∩ ( Q ∪ R )’.
[3 marks]
Answer:
(a)
ξ
P Q
R
(b)
ξ
P
Q
R](https://image.slidesharecdn.com/module5-sets-090823035141-phpapp02-130409040044-phpapp02/85/Module5-sets-090823035141-phpapp02-1-320.jpg)
![PPR Maths nbk
2. The Venn diagram in the answer space shows sets J ,K and L.
In the answer space, shade
(a) J ∩ L’
(b) (K ∪ L)∩ J’
[3 marks]
Answer:
(a)
J
L
(b) J K
L](https://image.slidesharecdn.com/module5-sets-090823035141-phpapp02-130409040044-phpapp02/85/Module5-sets-090823035141-phpapp02-2-320.jpg)
![PPR Maths nbk
3 The Venn diagram in the answer space shows set P, set Q and set R with the
universal set ξ = P ∪ Q ∪ R.
On the diagram in the answer space, shade
(a) P∪Q ∩R
(b) P ∩ ( Q ∪ R) ′
[3 marks]
Answer:
(a) Q
P R
(b) R
P
Q](https://image.slidesharecdn.com/module5-sets-090823035141-phpapp02-130409040044-phpapp02/85/Module5-sets-090823035141-phpapp02-3-320.jpg)
![PPR Maths nbk
4. Diagram 4 shows an incomplete Venn diagram that represents the number of
students from a class of 30, according to the subjects they have studied.
Each student studied at least one of the three subjects Physics, Chemistry
and Biology.
Given the universal set, ξ = P ∪ C ∪ B,
P = {students who studied Physics}
C = {students who studied Chemistry}
B = {students who studied Biology}
C P
6
5 2 1
B
DIAGRAM 4
20 students studied Chemistry and 12 students studied Biology. Based on this
information, find
(a) the number of students who studied Chemistry and Biology but not
Physics.
(b) the number of students who studied Biology only.
(c) the number of students who studied Physics.
[4 marks]
Answer:
(a)
(b)
(c)](https://image.slidesharecdn.com/module5-sets-090823035141-phpapp02-130409040044-phpapp02/85/Module5-sets-090823035141-phpapp02-4-320.jpg)
![PPR Maths nbk
5. (a) Given that ξ = { x: x is an integer and 7 ≤ x ≤ 15},
A = { x: x is a multiple of 3 },
B = {x : x is an odd number} and
C = { x: 10 ≤ x ≤ 13 }.
(a). List the elements of the set C ′ .
(b). Find n(A ∪B).
[3 marks]
6. Given that n(ξ) = 50. G and H are two sets for which n( G ∩ H) = 6,
n(G) = 18 and n(H) = 14.
(a). Draw a Venn diagram to represent the relationship between sets G
and H and write the number of elements in each region.
(b). Find n(G ∪ H)′.
[3 marks]
Answer:
(a)
(b)](https://image.slidesharecdn.com/module5-sets-090823035141-phpapp02-130409040044-phpapp02/85/Module5-sets-090823035141-phpapp02-5-320.jpg)
![PPR Maths nbk
7. If ξ = {x : 1 ≤ x ≤ 10 , x is an integer}
E = {x : x is a multiple of 4}
F = {x : x is a factor of 20}
(a) List all the elements in set E,
(b) Find n( E ∪ F ) .
[3 marks]
8. The Venn diagram in the answer space shows set P, set Q dan set R. On the
diagram, shade
(a) P ∩ Q’
(b) R ∩ (P’ ∪ Q)
[ 3 marks ]
Answer :
(a)
ξ
P
R
Q
(b)
ξ
P R
Q](https://image.slidesharecdn.com/module5-sets-090823035141-phpapp02-130409040044-phpapp02/85/Module5-sets-090823035141-phpapp02-6-320.jpg)
Module5 sets-090823035141-phpapp02
- 1. PPR Maths nbk MODUL 5 SKIM TUISYEN FELDA (STF) MATEMATIK SPM “ENRICHMENT” TOPIC : SETS MASA : 1 JAM 1. The Venn diagram in the answer space shows the universal set ξ, sets P, Q and R. The universal set ξ = P ∪ Q ∪ R. On the diagram in the answer space, shade the region for (a) P ∩ Q, (b) P ∩ ( Q ∪ R )’. [3 marks] Answer: (a) ξ P Q R (b) ξ P Q R
- 2. PPR Maths nbk 2. The Venn diagram in the answer space shows sets J ,K and L. In the answer space, shade (a) J ∩ L’ (b) (K ∪ L)∩ J’ [3 marks] Answer: (a) J L (b) J K L
- 3. PPR Maths nbk 3 The Venn diagram in the answer space shows set P, set Q and set R with the universal set ξ = P ∪ Q ∪ R. On the diagram in the answer space, shade (a) P∪Q ∩R (b) P ∩ ( Q ∪ R) ′ [3 marks] Answer: (a) Q P R (b) R P Q
- 4. PPR Maths nbk 4. Diagram 4 shows an incomplete Venn diagram that represents the number of students from a class of 30, according to the subjects they have studied. Each student studied at least one of the three subjects Physics, Chemistry and Biology. Given the universal set, ξ = P ∪ C ∪ B, P = {students who studied Physics} C = {students who studied Chemistry} B = {students who studied Biology} C P 6 5 2 1 B DIAGRAM 4 20 students studied Chemistry and 12 students studied Biology. Based on this information, find (a) the number of students who studied Chemistry and Biology but not Physics. (b) the number of students who studied Biology only. (c) the number of students who studied Physics. [4 marks] Answer: (a) (b) (c)
- 5. PPR Maths nbk 5. (a) Given that ξ = { x: x is an integer and 7 ≤ x ≤ 15}, A = { x: x is a multiple of 3 }, B = {x : x is an odd number} and C = { x: 10 ≤ x ≤ 13 }. (a). List the elements of the set C ′ . (b). Find n(A ∪B). [3 marks] 6. Given that n(ξ) = 50. G and H are two sets for which n( G ∩ H) = 6, n(G) = 18 and n(H) = 14. (a). Draw a Venn diagram to represent the relationship between sets G and H and write the number of elements in each region. (b). Find n(G ∪ H)′. [3 marks] Answer: (a) (b)
- 6. PPR Maths nbk 7. If ξ = {x : 1 ≤ x ≤ 10 , x is an integer} E = {x : x is a multiple of 4} F = {x : x is a factor of 20} (a) List all the elements in set E, (b) Find n( E ∪ F ) . [3 marks] 8. The Venn diagram in the answer space shows set P, set Q dan set R. On the diagram, shade (a) P ∩ Q’ (b) R ∩ (P’ ∪ Q) [ 3 marks ] Answer : (a) ξ P R Q (b) ξ P R Q
- 7. PPR Maths nbk MODULE 5 – ANSWERS TOPIC: SETS 1 (a) ξ 1 PQ R (b) ξ P Q R 2 2 (a) J ∩ L′ 1 J K (b) (K ∪ L ) ∩ J ′ 2 J K 3 L 3 Q (a) 1 P R (b) P R 2 3 Q
- 8. PPR Maths nbk 4 (a) 5 1 (b) 30 –(5 + 6 + 2 + 1 ) 1 16 1 (c) 9 1 4 5 (a) {10,11,12,13 } 1 (b) A = {9,12,15 } B = {7,9,11,13,15} A ∪ B = {7,9,11,12,13,15} 1 1 3 N(AUB)=6 6 (a) ξ 2 G H 24 12 6 8 (b) 24 1 3 7 (a) {4 , 8} 1 Note: Accept without bracket. (b) 6 2 3
- 9. PPR Maths nbk 8 ξ 1 P R 2 Q 3 P R Q