This document provides two examples of using Venn diagrams to solve problems involving sets. The first example involves students taking Filipino and Hekasi courses. It is determined that 11 students take Filipino only, 5 take Hekasi only, and 7 do not take either. The second example surveys coffee drinker preferences at a company. It finds that 16 like cream only, 35 like sugar only, and there are a total of 71 employees.

2. Let us apply the four set operations that we
have discussed in problem solving.

3. Example 1. In a class of 31, 19 are taking Filipino, 13 are taking
Hekasi and 8 are taking both subjects.
 a. How many students are taking
Filipino only?
 b. How many are taking Hekasi
only?
 c. How may doesn’t take any of
the two subjects?
Let n(F) = 19
n(H) = 13
n(F ∩ H ) = 8

4. The Venn Diagram for this problem is shown below.
Let n(F) = 19
n(H) = 13
n(F ∩ H ) = 8
Base on the Venn diagram, we have the following:
a. There are 11 students who are taking Filipino
only.
b. There are 5 who are taking Hekasi only.
c. Seven (7) doesn’t take any of the two subjects.

5. Example 2. In a survey made to all employees in a certain company
who are coffee lovers, the following information was found.
36 likes coffee with cream
55 likes coffee with sugar
20 likes both
• a. How many likes cream only?
• b. How many likes sugar only?
• c. How may employees are there in all?
Let n(Cream) = 36
n(Sugar) = 55
n(Sugar ∩ Cream) = 20

6. Let n(Cream) = 36
n(Sugar) = 55
n(Sugar ∩ Cream) = 20
Based on the Venn diagram we have the
following:
1. The are 16 employees likes cream only.
2. There are 35 employees likes sugar only.
3. There are 71 employees in a certain building.