CHAPTER-9
VENN DIAGRAM
The term venn Diagram relates to the different type of figures drawn to represent relationship between two or more objects. These figures represent by a circle, triangle, square and rectangle. The concept of venn diagram originates from set theory. A basis concept of set, subset, disjoint set can help to understand the concept of venn diagram. To understand these terms, we are given following points with examples.
Example 1. An object is said to have an intersection with the other object, when two objects share something in common.
For Examples:
(a) Dogs, Pets
(b) Fathers, Brothers
(c) Clerks, Government Employees
Example 2. An object is said to be a subset of another object, if former is a part of latter.
For examples:
(a) Minutes, Hours
(b) Females, Mothers
(c) Engineers, Human Beings
Example 3. An object is said to be disjoint with other, when two objects share nothing in common.
For examples:
(a) Table, Chair
(b) Doctors, Engineers
(c) Human Beings, Rates
Directions (Qs. 1-4) : Each of the se questions below contains three group of things. You are to choose from the following fine numbered diagrams, a diagram that depicts the correct relationship among the three groups of things in each questions.
1. Tables, Chairs, Furniture
2. Tie, Shirts, Pantaloon
3. Dogs, Pets, Cats
4. Brinjal, Meat, Vegetables
SOLUTIONS
1. (d) Tables and chairs are unrelated items, but both are the items of furniture.
2. (c) Tie, shirt and pantaloon are separated items.
3. (d) Dogs and cats are entirely different from each other. But both are pet animals.
4. (e) Brinjal is a vegetable. But meat is entirely different.
Example 5. Which one of the following diagrams correctly represents the relationship among the classes: Judge, Thief, Criminal.
Solution (b) All thieves are criminal. But judge is entirely different.
Example 6. Which one of the following sets is best represented in the adjoining diagram?
(a) Animals, Insects, Cockroaches
(b) Country, States, Districts
(c) Animals, Mates, Females and Hermaphrodities
(d) States Districts,
Solution (d). Districts from the part of the state but, union territory is entirely different.
Example 7. In the following diagram, the square represents girls, the circle represents tall persons, the triangle is for tennis players and the rectangle stands for the swimmers. On the basis of the above diagram, answer the following questions.
1. Which letter represents tall girl, who do not play tennis and are not swimmers?
(a) E
(b) G
(c) D
(d) C
2. Which letter represents girls who are swimmers, play tennis but are not tall?
(a) F
(b) B
(c) E
(d) None of these
3. Which letter represents tall persons who are gents and swimmers but do not play tennis?
(a) J
(b) K
(c) L
(d) I
4. Which letter represents tall girls who are swimmers but don’t play tennis?
(a) H
(b) G
(c) D
(d) C
SOLUTION
1. (c). Tall girls are represented by the region common to the square and the circle i.e., D, C, G, and H. But according to the given conditions, the girls are neither a part of rectangle nor the triangle. So, Answer is D.
2. (d). Girls, who are swimmers and play tennis are represented by the region i.e., H. But according to the given condition girls should not be tall. So, required region should not be a part of the circle. Since, it is a part of the circle, hence the answer is none of these.
3. (b). Tall persons are represented by regions inside the circle i.e., C, D, G, H, I, J and K. Since persons are not girls and do not play tennis, so the region should not be a part of either the square or the triangle. So, C, D, G, H should be excluded. Also according to the given conditions, the persons should be swimmers. So, the required region should be a part of the rectangle. Hence, the answer is K.
4. (b). Tall girls who are swimmers are represented by the region common to the square, circle and the rectangle i.e., G and H. But according to the given conditions, girls should not be tennis players. So, the required region should not be apart of the triangle, so H should be excluded. Hence, the answer is G.
Example 8. Read the figure and find the region representing persons who are educated and employed but not confirmed.
(a) b, d
(b) a, b, c
(c) a, c
(d) a, d, c
Solution (a). The required region is the one which is common to the circles but lies outside the triangle. So the answer is b and d.
Direction for Questions 1 to 3:
In a class of 150 students 55 speak English; 85 speak Telugu and 30 speak neither English nor Telugu.
1. How many speak both English and Telugu?
(a) 10
(b) 120
(c) 20
(d) 45
2. How many speak only Telugu?
(a) 85
(b) 55
(c) 95
(d) 65
3. How many speak at least one of the two languages from English & Telugu?
(a) 110
(b) 120
(c) 130
(d) 100
Directions for Questions 4 and 5:
A class of 30 students comprises boys who can play Cricket, Hockey and Football. 3 boys play only cricket, 3 bys play only Hockey and 2 play only football. 4 boys could play all three games, while 11 could play Football and Cricket, and 10 boys could play Football and Hockey.
4. How may boys played Cricket and Hockey but not Football?
(a) 1
(b) 2
(c) 3
(d) 5
5. How many boys can play atleast two games?
(a) 16
(b) 18
(c) 10
(d) 22
Directions for Questions 6 to 9:
In a class, 70 students passed in Mathematics, 50% of the students passed in English, 25% of the students passed in both and 5% of the students passed in neither Mathematics nor English.
6. How many students are there in the class?
(a) 93
(b) 145
(c) 100
(d) 140
7. How many students passed in only one subject?
(a) 75
(b) 53
(c) 80
(d) 70
8. How many students failed in atleast one subject?
(a) 5
(b) 25
(c) 50
(d) 75
9. What is the ratio of the number of students who passed in English to that in Mathematics?
(a) 1 : 1
(b) 2 : 3
(c) 5 : 7
(d) 10 : 9
Directions for Questions 10 to 13:
In a survey of 150 readers it has been found that 75 read newspaper A, 90 read newspaper B ad 70 read newspaper C. 40 read A and B; 35 read B and C; 30 read A and C and 10 read all the three.
10. How many respondents read none of the newspapers?
(a) 30
(b) 20
(c) 10
(d) 40
11. How many read exactly two newspapers?
(a) 75
(b) 105
(c) 95
(d) 85
12. How many read exactly one newspaper?
(a) 35
(b) 55
(c) 235
(d) 120
13. How many read neither A nor B?
(a) 45
(b) 70
(c) 110
(d) 15
Directions for Questions 14 to 17:
Scholars colony has a population of 2800 members.
Number of members reading only English newspaper = 650
Number of members reading only Hindi newspaper = 550
Number of members reading only Marathi newspaper = 450
Number of members reading all three newspaper = 100
Number of members reading Hindi as well as English newspaper = 200
Number of members reading Hindi as well as Marathi newspaper = 400
Number of members reading English as well as Marathi newspaper = 300
14. Find number of members reading Hindi newspaper?
(a) 950
(b) 1050
(c) 650
(d) 550
15. Find number of members reading none of the newspapers?
(a) 450
(b) 550
(c) 2550
(d) 2650
16. Find number of members reading only one newspaper?
(a) 450
(b) 1100
(c) 1600
(d) 1650
17. Find number of members reading atleast two newspapers?
(a) 400
(b) 500
(c) 600
(d) 700
Directions for Questions 18 to 21:
The following table gives the statistics of a class in which each student opted for Maths or Statistics or both. Unfortunately most of the figures have been erased but I remember some information.
| | Maths | Statistics | Both | Total |
| Male | 50 | | | |
| Female | | | | |
| Total | | 70 | | 150 |
The information is as follows:
1. 13 1/3% of the students took both Maths and Statistics
2. 40% of the students were females.
3. None of the females took both Mathematics and Statistics.
Fill the table and answer the following Questions.
18. How many males took both Mathematics and Statistics?
(a) 40
(b) 10
(c) 20
(d) 60
19. How many students took only Mathematics?
(a) 50
(b) 80
(c) 60
(d) 10
20. How many males took only Statistics?
(a) 0
(b) 40
(c) 20
(d) 30
21. How many females took only Mathematics?
(a) 10
(b) 50
(c) 70
(d) 40
Directions for Questions 22 to 25:
In a class of 160 students, it was found that 65 play Cricket 70 play Hockey and 90 play Football, 30 play Cricket and Hockey, 40 Cricket and Football, 35 play Hockey and Football and 15 play none of these three games.
22. How many play all three games?
(a) 745
(b) 105
(c) 25
(d) 55
23. If 10 students who play only Hockey now start playing Cricket also; and 10 students who play only football stop playing Football and start playing Cricket how many will play both Cricket and Hockey?
(a) 30
(b) 40
(c) 20
(d) 55
24. How many students play exactly one game?
(a) 90
(b) 75
(c) 105
(d) 145
25. If 5 students stop playing Hockey and start playing Cricket, what is the least number of students playing only Football and Hockey but not Cricket?
(a) 15
(b) 30
(c) 10
(d) 5
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