The document discusses problems involving sets and operations on sets such as union and intersection. It provides two word problems as examples: 1) A class of 40 students where some prefer Japanese language, Korean language, or both. It asks how many students prefer each language in total or exclusively. 2) A survey of 50 people on ice cream flavors they like from chocolate, mango, and strawberry. It asks how many people like each flavor alone or in certain combinations. The document shows the set diagrams and calculations to arrive at the answers.

1. SOLVE PROBLEMS
INVOLVING SETS
MODULE 7

2. OR - UNION
AND -
INTERSECTION

3. •Consider this problem:
In a class of 40, 12 students
prefer taking Japanese
Language as elective subject,
15 prefer Korean language,
and 8 like to learn both

4. 40 students - Total
12 students – Japanese
Language
15 students - Korean language
8 students - Both languages.
𝟏𝟐 − 𝟖
𝑩𝒐𝒕𝒉
𝟏𝟓 − 𝟖
𝟒𝟎 − 𝟏𝟗

5. 1. How many students prefer Japanese
or Korean language?
There are 19 students prefer Japanese or Kore

6. 2. How many students prefer Korean
language but not the Japanese
language?
There are 7
students
prefer Korean
Language but
not Japanese
Language.

7. 3. How many students prefer only one
of the two languages?
There are 11 students prefer only one of the t

8. 4. How many students prefer neither
of the two languages?
Total → 𝟒𝟎
𝐉 ∪ 𝐊 → 𝟏𝟗
𝟒𝟎 − 𝟏𝟗 = 𝟐𝟏
There are 21 students prefer neither of the tw

9. •Consider another problem:
A survey was conducted with 50
people on the ice cream flavor they
like. It was found out that 28 likes
chocolate, 15 likes mango, and 20
likes strawberry. Furthermore, 8 likes
chocolate & strawberry, 11 likes
mango & strawberry, 7 likes chocolate

10. 50 → Total people
28 → Chocolate
15 → Mango
20 → Strawberry
8 → Chocolate &
Strawberry
11 → Mango &
Strawberry
7 → Chocolate &
Mango
4 → 3 flavors
C
S
M
U
43
7
4
5
1
17
17+4+4+3+1+7+5
=41 9

11. How many people likes:
1. Chocolate only
2. Strawberry only
3. Mango Only
4. Chocolate & Strawberry but not
Mango
5. None of the flavors

12. The number of people who likes:
1. Chocolate only is 𝟐𝟖 − 𝟏𝟏 = 𝟏𝟕
2. Strawberry only is 𝟐𝟎 − 𝟏𝟓 = 𝟓
3. Mango only is 𝟏𝟓 − 𝟏𝟒 = 𝟏
4. Chocolate & Strawberry but not
Mango is
𝟏𝟕 + 𝟒 + 𝟓 = 𝟐𝟔