This document provides examples of using Venn diagrams to solve word problems involving sets. It includes two examples: 1) A group of 10 children where some like cartoons and comics. 2) Among 70 doctors, some work in hospitals and their own homes. It explains how to draw the Venn diagrams and use set formulas to calculate unknown values, such as the number of children who don't like cartoons or comics or the number of doctors who don't work in either location. Four additional practice problems are provided at the end.

1. The indicators of learning : determining to solve the problem students
be able determine to solve the problem by using concept in problem
solving
U = { 1,2,3,4,5,6,7,8,9,10}
P = { 3,4,5 }
Q = { 4,5,6,7}
Draw the venn diagram
U
P
Q
.3
.4
.5
.1
.2
.6
.7
.10
.9
.8

2. There are ten children in a group , they are Akbar, Arsya , Dea , Eldico , Hasna, Hilda ,
Ivan , Jihan , Kasiam, alif
Five children who like cartoon , they are Akbar , Arsya , Dea , Eldico, Hasna
Three children who like comics , there are Hilda, Akbar , Eldico
The other children who don’t like either cartoon or comics .
U
B
A
.1
.3
.2
.4
A.= The set of children who like cartoon
B = The set of the children who like comics

3. n(AB)=2
n ( A) = 3 + 2 = 5
n ( A  B )’ = 4
n (U ) = 10
n (U) = n (A) + n (B) – n (A  B) + n ( A  B )’

4. Example :
Among 70 doctors in a town , 40 doctors work in hospital , 43 doctors work in their
own house , and 15 doctors work both in a hospital and their own house !
Find the number of doctors who don’t work either in a hospital or in the own house
Known : n ( U ) = 70
n ( H ) = 40
n ( O ) = 43
n ( H  O ) = 15
Unknown : n ( H  O ) ‘ = …..?

5. Solution : H = The set of doctors who work in hospital
O = The set of the doctors who work in their own house
U
O
H
.28
.25
.15
.2
n ( U) = n (H) + n (O) – n ( H  O) + n ( H  O ) ‘
70 = 40 + 43 – 15 + n ( H  O ) ‘
70 = 68 + n ( H  O ) ‘
n ( H  O ) ‘ = 70 – 68
n(HO)‘=2
so, the number of doctors who don’t work either in a hospital or in their house is 2
doctors

7. EXERCISE
1. There are 40 students in a class , where 25
students wear rings, 20 students wear earrings,
and 11 students wear both rings and earrings. Find
the number of students who wear neither rings nor
earrings ?
2. There are 70 children in ahostel. Among these
children, 35 children can speak English, 8 children
can speak both English and Chinese, and 11
children can’t speak either English or Chinese. Find
the number of children can speak Chinese ?
3. Of a number of children given that 25 children who
like play piano . 21 children who like play guitar
and 9 children who like both of them . The number
of children in that group is….
4. Of a group of 46 students , 33 students who like
green color , 27 students who like yellow color and
12 students who don’t like either green or yellow .
The number of students who like both green and
yellow is….