Page 160 - Mathematics_Form_Two

Sets
(b) The number of students who study
FOR ONLINE READING ONLY
(a) Elements of B only = 6 – 4 = 2.
Mathematics for Secondary Schools (b) A ⊂ B. This is because all elements
Therefore, B has 4 + 2 = 6 elements.
in set A are contained in set B.
Example 7�24
In a class of 120 students, 40 study
English, 60 study Kiswahili, and 30
study both Kiswahili and English. Find
the number of students who study:
(a) English only.
(b) Neither English nor Kiswahili.
Solution
Let = {All students in the school}
E = {All students who study English}
K = {All students who study Kiswahili}
Representation of the three sets in a
Venn diagram is as follows.
Given n(E∩K) = 30, n(E) = 40, and
n(K) = 60.
(a) The number of students who study
English only is given by:
154
MATHEMATIC F2 v5.indd 154
MATHEMATIC F2 v5.indd 154
n (E ∩ K ) ′ = n (E) n− (E ∩ K)
= 40 – 30 = 10
Therefore, 10 students study English
only.
Kiswahili only is given by:
= 60 – 30 = 30
(K) n−
n
K)
(E ∩
n
(K ∩
E ) ′ =
The number of students who study
English or Kiswahili or both are:
30+30+10 = 70
who study neither Kiswahili nor
Therefore, the number of students
English are:
120 – 70 = 50 students.
Example 7�25
In a certain school, 50 students eat
meat, 60 eat fish, and 25 eat both meat
and fish. Assuming that every student
eats meat or fish, find the total number
of students in the school.
Solution
Let = {All students in the school},
M = {All student who eat meat}, and
F = {All students who eat fish}.
The Venn diagram representing these
information is as follows:
From the Venn diagram, total number
of students = 25 + 25 + 35 = 85.
Therefore, there are 85 students in the
school.
Student's Book Form Two
11/10/2024 20:13:33
11/10/2024 20:13:33