This document discusses solving problems involving sets using Venn diagrams. It provides examples of word problems involving sets and their solutions. Some examples include problems about students' favorite subjects, places people like to stay, sports students like, and dances guests participated in at a party. The document aims to teach how to represent sets visually using Venn diagrams and solve problems involving intersections and unions of different sets.

1. SETS
Problem Solving
Involving Sets
Marites G. Ablay

2. OBJECTIVES
1.solve set operations and problems involving
set with use of Venn diagram.
2. apply the knowledge in sets in solving
problem related in sets.
3. show cooperation in class discussion.

3. REVIEW
A class is composed of 40 students and they have 3
favorite subjects.
 1. How many students like the 3 subjects?
a. 4 b. 5 c. 6 d. 7
 2. How many students like Math and Science only?
a. 4 b. 5 c. 6 d. 7
 3. How many students like English and Science only?
a. 4 b. 5 c. 6 d. 7

4. A class is composed of 40 students and they have 3 favourite
subjects.
 4. How many students like Math and English but not Science?
a. 5 b. 6 c. 7 d. 8
 5. How many students like Math only?
a. 5 b. 6 c. 7 d. 8
 6. How many students like Math ?
a. 21 b. 22 c. 23 d. 24

5. DEVELOPMENT OF THE LESSON
I. A teacher announces that out of 35 students in class, 25 passed both
the Math and Science tests, 30 passed the Math test, and 28 passed the
Science test.
1. How many students pass Math test only?
Answer : 5
2. How many students pass Science test only?
Answer : 3
3. How many students did not pass either Math or
the Science test?
Answer : 2
255 3

6. B. 100 people were surveyed on the places they like to stay. Suppose B =
{people who like beaches}, M = {people who like mountains}, and C = {people
who like big cities}
 76 people like beaches
 53 people like mountains
 44 people like big cities
 42 people like beaches and mountains
 15 people like mountains and big cities
 31 people like beaches and big cities
 10 people like the 3 places
Questions:
 How many people staying in
 a. big cities only?
 b. mountains and beaches?
 c. mountains and beaches but not big cities?
 d. beaches and big cities but not mountains?
 e. All three.

7. Generalization
How do we solve problem solving involving sets.

8. GROUP ACTIVITY:
Solve the following problem using the Venn diagram:
1. Of the 150 students in Grade 7, 45 are in the
Damath Club, 65 are in Sudoku Club and 20 are
in both Damath and Sudoku Club. How many
students are:
a. In Damath Club only?
b. In Sudoku Club only?
c. In Damath or Sudoku Club?
d. not in Damath nor Sudoku Club?

9. 2. A Group of students were given questionnaires to find out
what sports they like. It was found out that:
84 like basketball 58 like basketball and volleyball
80 like volleyball 47 like basketball and tennis
65 like tennis 42 like volleyball and tennis
25 like the three sports
Questions:
a. How many like basketball only?
b. How many like volleyball only?
c. How many like tennis only?
d. How many like basketball and volleyball but not tennis?
e. How many like basketball and tennis but not volleyball?
f. How many like volleyball and tennis but not basketball?
g. How many students are there in all?

10. 3. Antonio J. Villegas High School Team selected 50
players to compete in the coming Division meet. The set of
players who will participate in the games are
 24 – basketball
 30 – softball
 22 – track & field
 18 - basketball and track & field
 12 – softball and track & field
 12 – basketball and softball
 8 – will participate in all the three games
a. How many players will play softball only?
b. How many players will play basketball only?
c. How many players will play track & field only?
d. How many players will not play?

11. 4. Joan’s birthday party was very lively one. 130
guests were present. They even had a contest on the
following dances: Cha-cha, Tango and Waltz. Those
who joined in the contest were as follows:
 58 – danced the Chacha
 62 – danced the Tango
 50 – danced the Waltz
 22 – danced the Chacha and the Tango
 20 – danced the Tango and the Waltz
 18 – danced the Chacha and the Waltz
 12 – danced all the three
a. How many did not dance at all?
b. How many danced the chacha only?
c. How many danced the Tango only?
d. How many danced the Waltz only?

12. Evaluation
Answer the following.
1. A group of 25 high school students was asked whether
they use either Facebook or Twitter or both. Fifteen of these
students use Facebook, and twelve use Twitter.
How many use Facebook only?
How many use Twitter only?
How many use both social networking sites?
2. Among the 70 kids in Grade Seven, 53 like eating in
Jollibee, while 42 like eating in McDonalds. How many like
eating both in Jollibee and McDonalds? In Jollibee only? In
McDonalds only?