Page 11 - Spotlight A+ Form 4 & 5 Mathematics KSSM

Form
4 Mathematics Chapter 4 Operations on Sets

(b) Solve problems involving the union of sets
ξ
●6 ●19 ●18
A Example 14
●7 B ●17
●10
●5 A residential area has 105 families. A total of 40
●8 ●20
●15 ●16 families own motorcycles. The number of families
that own cars only is twice the number of families
●9
●11 ●12 ●13 ●14 that own motorcycles only. The number of families
that own motorcycles and cars are the same as the
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CHAP. Try question 4 in Formative Zone 4.2 number of families that do not own motorcycles
or cars.
4 (a) Draw a Venn diagram to show the information
above.
(b) Hence, determine the number of families that
own motorcycles or cars.
Operations on sets
https://bit.ly/2IRwsBs Solution:
(a)  = {families in the residential area}
A = {families that own motorcycles}
B = {families that own cars}
Example 13
ξ
Given the universal set  = {x : 4 < x , 16, A B
x is an integer}, P = {x : x is a perfect square}, x y 2x
Q = {x : x is a multiple of 3} and R = {x : x is a prime y
number}.
(a) Determine n[(P < Q < R)].
(b) Shade the region that represents (P < Q < R) n(A) = 40
on a Venn diagram. x + y = 40 ....... a
n() = 105
Solution: x + y + 2x + y = 105
(a)  = {4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15} 3x + 2y = 105 ..... b
P = {4, 9} a × 2, 2x + 2y = 80 ....... c
Q = {6, 9, 12, 15} b – c, x = 25
R = {5, 7, 11, 13}
P < Q < R = {4, 5, 6, 7, 9, 11, 12, 13, 15} From a, 25 + y = 40
(P < Q < R) = {8, 10, 14} y = 15
n[(P < Q < R)] = 3 ξ
A B
Alternative Method
25 15 50
n() = 12
n(P < Q < R) = 9 15
n[(P < Q < R)] = 12 – 9
= 3 (b) n(A < B) = 25 + 15 + 50
(b) = 90
ξ The number of families that own motorcycles
P Q or cars is 90.
●6
●4 ●9 ●12 Try question 6 in Formative Zone 4.2
●15
●8 ●14
●5 ●7
●10 ●11
●13 R

Try question 5 in Formative Zone 4.2

78 4.2.2 4.2.3

ENG04 Spotlight Matematik F4.indd 78 14/01/2021 9:53 PM