Page 155 - Mathematics_Form_Two

Sets

(d) Required to find (Cn ∪ P) . ′ n (W ∩ S ) ′ = 240 150−
+
n ( )µ = n (C∪ P) n (C∪ P)′ 90= (have clean water only)
(W ∩(S) =
500 370 n= + (C∪ P)′ But (S)nn = n n (W ∪ (Wn S)+ (Wn (W)+ (S)n= ∩ n ′∩ S) S)+ (W′∩ n S) − S). n (W ∩ S)
+
(Cn ∪ P)′ = 500 370− 220 150+ (Wn=S)n 220 == n (Wn (W)+n S) (S) n− S) (W ∩ S)
′∩ ′∩
+150+
(W ∪
130= (Wn ′∩ S) = 220 150−
FOR ONLINE READING ONLY
Therefore, 130 people are in neither of the = 70 (have sanitation only)
the two groups.
Households with only one service = clean

water only + sanitation only
Example 7�16 90 70= +
In a village with 400 households, 240 160= Mathematics for Secondary Schools
have access to clean water and 220 Therefore, 160 have only one of these
have good sanitation. If 90 households services.
have no access to clean water and good
sanitation, how many households have: Exercise 7�4
(a) Both clean water and good sanitation.
(b) Only one of these services. From question 1 to 10 find the union and
Solution intersection of the given sets.
}
=
=
Let µ = {households in a village , 1. A {5, 10, 15}, B {15, 20}
W = {households with acces to clean water}, 2. A { }, B {14, 16}
=
=
}
S = {households with sanitation .
3. A = {first five letters of the English
Given ( )n µ = 400, (W)n = 240, alphabet}, B ={a, b, c, d, e}
′
n (S) = 220, and (Wn ∪ S) =90.
=
(a) Required to find (Wn ∩ S) = . 240 220 310+ − 4. A ={counting numbers}, B {prime
( )n µ = n (W ∪ S) n (W ∪ S)′ numbers}
+
400 n= (W ∪ S) 90+ 5. A ={cup, spoon}, B ={cup, plate}
400 = n (W ∪ S) 90+ = 400 90−

310= 6. A ={All multiples of 5 less than 30},
+n
But (Wn (Wnn n ∪ ∪(W ∪ (W (W)+ (S)n(W)+n(W)+ (S)nS) = (W)+ (S)n+ −(S) − (W − n n nnn)+ − (W ∩(W ∩(W ∩ (S)n(Wn − S)S)S)(Wn S)∩ ∩ S) B ={All multiples of 10 less than
S) = S) = S) = ∪
+
+
+(W=
nnn∪S)
30}
310 240 220 n= + − − n (C∩ (W ∩ P) S)
(Wn ∩ S) = 240 220 310+ − 7. A={All prime factors of 42},
=
460 310= − B {All prime factors of 15}
150= 8. A ={All even numbers less than 10},
Therefore, 150 households have both B ={All multiples of 3 less than 12}
clean water and good sanitation.

nn n n (W ∪ (Wn S)+ (Wn (W)+ (S)n= ∩ n ∩ S) S)+ (W ∩ S ) ′ n ) −S′ n (W ∩ S) 9. A = {64, 81, 100, 121},
(W) =
(W ∩ (W) =
+
240 150+ (Wn= S)n 240 150+ (Wn= = n (W)+ S ) ′ (S) n−S ) ′ S) B = {64, 81, 144}.
∩n ∩
(W ∪
(W ∩
+
149
Student's Book Form Two
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MATHEMATIC F2 v5.indd 149