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**VENN DIAGRAM**

**How to solve problems involved**

**Venn Diagram**

**Steps based on the given problem:**

1. Check for the first most intersections involved in the problem. (i.e A Ω B Ω C )

2. Check for the second most intersections involved in the problem. (i.e A Ω B )

3. Based on the example below 10 has three intersections which is most common. That is lobby Ω library Ω cafeteria.

Examples

1. A group of 48 students were asked on their favorite places inside the school campus where they stay during vacant time. The results are as follows.

34 stays at the library

30 stays at the lobby

27 stays at the cafeteria

18 stays at library and lobby

20 stays at library and cafeteria

16 stas at lobby and cafeteria

10 stays at all places, library, lobby and cafeteria

Questions:

1. How many students stay at Library only?

2. How many students stay at lobby only?

3. How many students stay at cafeteria only?

4. How many students did not stay at three places mentioned?

2. A group of 75 students were asked on what subjects they like and the following results were obtained.

32 students like Math

29 students like English

31 Students like Spanish

11 students like Math and Spanish

9 students like English and Spanish

7 students like math and English

3 students like the three subjects

Questions:

a. How many likes Spanish only?

b. How many likes Math only?

c. How many likes English only?

d. How many do not like any of the three subjects?

3. A group of 48 college students were asked on their preferences computer subjects and the results came out to be:

30 prefer computer science

27 prefer information technology

34 prefer information system

18 prefer computer science and information technology

20 prefer computer science and information system

16 prefer information tech and information system

10 prefer the three types

Questions:

1. How many prefers computer science only?

2. How many prefers information technology only?

3. How many prefers information system only?

4. How many do not prefer any of the three subjects?

4. Fifty-five students in a certain school were asked what mathematics subjects they like most and the following results were obtained.

32 likes Algebra

29 likes Calculus

31 likes Geometry

11 likes Algebra and Geometry

9 likes Calculus and Geometry

7 likes Algebra and Calculus

3 likes the three subjects

Questions:

1. How many likes Algebra only?

2. How many likes Calculus only?

3. How many likes Geometry only?

4. How many don't like any of the three subjects?

Problem

**(two sets):**
1. Out of 30
students, 12 are taking Physics and 18 are
taking Chemistry. 5 are taking both subjects, how many students are not taking
any subject?

*Answer*