VENN DIAGRAM

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

Five students are not taking any subjects