Page 154 - Mathematics_Form_Two

Sets

From Activity 7.3, one may have learned Example 7�15
that, the number of elements of a set can
be obtained by counting elements in the In a community of 500 people, 300 are
given set. The number of elements of a in the climate action group and 250 are
set A is denoted by (A)n and read as “the in a poverty alleviation group. If 180 are
number of elements in set A ”. in both groups, how many people are in
FOR ONLINE READING ONLY
For any two sets A and B, the following each of the following categories?
Mathematics for Secondary Schools n (A (A ∪ ( )µ = B) = n n(An (An n ∩ = + (A) n+ ′ B ) n+(B) n− ∩ B)+ (An ) n+ B)+ (An (A ∩ ′ ′ B ) ′∩B′ = B) B) Solution
(a) Climate action group only.
are the relationships between the two sets.
(b) Poverty alleviation group only.
1. n
(B) n−
(A ∩
(c) At least in one group.
(A ) ′
2. n
(A) n
(d) Neither of the two groups.
B ) ′
n
3. nB)∪
(A) = =
(A ∩ (A ∩
′ n
(A ∩ (A) n+
B ) ′
(A ) ′
∩ ′
4. n (A)n (A )n
B ) ′∩
(A′ =
{people in climate action group
C =

Example 7�14 Let: µ = {people in a community } } }
{people in poverty alleviation group
P =
A total of 40 people attending a seminar
were asked to describe the source of Given n() = 500, n(C) = 300,
energy between gas and charcoal they ( )nP = 250, and (nC ∩ P ) 180= .
use in cooking. Among them, 16 said
they use gas, 25 use charcoal and 6 use (a) Required to find (Cn ∩ P) . ′
neither gas nor charcoal. How many From (C)n = n (C∩ P) n+ (C∩ P ). ′
participants use both gas and charcoal? Thus, 300 180 n= + (C∩ P ). ′
Solution
}
Let µ = {people attended the seminar , n (C∩ P ) 300 180= ′ −
120=
}
G = {people who use gas , and Therefore, 120 people are only in
}
C = {people who use charcol . climate action group.

Thus, n( ) = 40, (G) 16,n = (C)n = 25, (b) Required to find (Cn ′∩ P).
′′
and (Gn (Gn ∪∪ C) =6.C) =6. (P)n = n (C∩ P) n+ (C′∩ P).

Required to find (Gn ∩ C) 16 25 34= + −
(Cn ′∩ P) = 250 180−
From (Gn ∪ C) = n ( ) nµ − (G ∪ C)′ 70=
40 6= − Therefore, 70 people are in poverty
= 34 reduction group.
But (Gn ∪ C) = n (G) n+ (C) n− (G ∩ C).
Rearranging the equation gives, (c) Required to find (Cn ∪ P) = . n (C) n+ (P) n− (C∩ P)
n (G ∩ C) = n (G) n+ (C) n− (G ∪ C) n (C∪ P) = n (C) n+ (P) n− (C∩ P)
n (G ∩ C) 16 25 34= + − 300 250 180= + −
= 7 370=
Therefore, 7 participants used both gas Therefore, 370 people are at least in
and charcoal. one group.

148
Student's Book Form Two

11/10/2024 20:13:20
MATHEMATIC F2 v5.indd 148
MATHEMATIC F2 v5.indd 148 11/10/2024 20:13:20