venn_diagrams-final.pdf

VENN DIAGRAMS

OBJECTIVE:

The main aim of this section is to test your ability about the relation between some items of agroup by diagrams.

In these questions some figures of circles and some words are given. You have to choose a figure whichrepresents the given words.

Some solved examples are given below:

Example 1:

If all the words are of different groups, then they will be shown by the diagram as given below.

Dog, Cow, Horse

All these three are animals but of different groups, there is no relation between them. Hence they will berepresented by three different circles.

Example 2:

If the first word is related to second word and second word is related to third word. Then they will be shownby diagram as given below.

Unit, Tens, Hundreds

Ten units together make one Tens or in one tens, whole unit is available and ten tens together make onehundreds.

Example 3:

If two different items are completely related to third item, they will be shown as below.

Pen, Pencil, Stationery

Example 4:

If there is some relation between two items and these two items are completely related to a third item theywill be shown as given below.

Women, Sisters, Mothers

Some sisters may be mothers and vice-versa. Similarly some mothers may not be sisters and vice-versa.

But all the sisters and all the mothers belong to women group.

Example 5:

Two items are related to a third item to some extent but not completely and first two items totally different.

Students, Boys, Girls

The boys and girls are different items while some boys may be students. Similarly among girls some may bestudents.

Example 6:

All the three items are related to one another but to some extent not completely.

Boys, Students, Athletes

Some boys may be students and vice-versa. Similarly some boys may be athletes and vice-versa. Somestudents may be athletes and vice-versa.

Example 7:

Two items are related to each other completely and third item is entirely different from first two.

Lions, Carnivorous, Cows

All the lions are carnivorous but no cow is lion or carnivorous.

Example 8:

First item is completely related to second and third item is partially related to first and second item.

Dogs, Animals, Flesh-eaters

All the dogs are belonging to animals but some dogs are flesh eater but not all.

Example 9:

First item is partially related to second but third is entirely different from the first two.

Dogs, Flesh-eaters, Cows

Some dogs are flesh-eaters but not all while any dog or any flesh-eater cannot be cow.

Example 10(Questions 10 to 12)

In the following diagram, the square represents girls, the circle tall persons, the triangle is for tennis playerand the rectangle stands for the swimmers

10. Which letter represents tall girls who are swimmers but don’t play tennis?

a.C b. F c. G d. H

Sol: Tall girls, who are swimmers, are represented by the region common to the square, circle and rectanglei.e., G and h. But, according to the given conditions, girls shouldn’t be a tennis player. So, the requiredregion should not be a part of the triangle i.e., H should be excluded. Thus, the region representing thepersons satisfying the given conditions is G. Hence, the answer is- c.

11. Which letter represents girls who are swimmers, plays tennis but are not tall?

a. B b. E c. F d. None of these

Sol: Girls who are swimmers and play tennis are represented by the region common to the square, triangleand rectangle i.e., H but, it is that the girls shouldn’t be tall. So, the required region should not be a part ofthe circle. Since h is a part of the circle, so the answer is- d

12. Which letter represents tall persons who are gents and swimmers but do not play tennis?

a .I b. J c. K d. L

Sol; The tall persons who are represented by regions inside the circle i.e., C,D,H,G,I,J and K. Since thepersons are not girls and do not play tennis, so the region should not be a part of either the square or thetriangle. Thus, C, D, H, G should be excluded. Also, according to the given conditions, the person should beswimmers. So, the required region should be a part of the rectangle and such a region is K. Hence, theanswer is- c.

Example 11(Questions 13 to 15)

In the following diagram, the rectangle represents artists, the circle represents players and the trianglerepresents doctors.

13. How many players are neither artists nor doctors?

a .3 b. 8 c.22 d. 25

Sol: The region lying inside the circle but outside the triangle represents the number of players who areneither artists nor doctors. It is 25. Answer is –d

14. How many artists are players?

a .30 b.29 c.25 d. 22

Sol: The region common to the circle and the rectangle represents the required set of persons. Thus, numberof artists who are players is 25. Answer is-c

15. How many doctors are both players and artists?

a .3 b.4 c.8 d. 11

Sol: The region common to the circle, triangle and the square represents the required set of persons. Thus,number of doctors who are both players and artists is 3. Answer is-a .

Exercise problems

1. Which of the following diagrams correctly represents Elephants, Wolves, Animals? I.A.S.1992

2. Which of the following diagrams correctly represents the relationship among the classes?

Carrot, Food, Vegetable I.A.S.1996

3. Directions (questions from 3 to 7): in the following questions, three classes are given. Out of the fourfigures that follow you are to indicate which figure will best represent the relationship amongst the three

3. Women, Mother, Widows

4. Authors, Teachers, Men

5. Sparrows, Birds, mice

6. Tea, Coffee, Beverages

7. Boys, students, athletes

8. Select from the given diagrams, the one that illustrates the relationship among the given three classes;

Judge, thief, criminal S.C.R.A.1994

9. Which of the following diagrams correctly represents the relationship among the classes:

Tennis fans, cricket players, students I.A.S.1990

10 Choose from the four diagrams given below, the one that illustrates the relationship among, French,German

11. Which of the following diagrams correctly represents the relationship among the classes:

Rhombus, quadrilaterals, polygons

12. Which of the following diagrams correctly represents the relationship among the classes

Musicians, Instrumentalists, Violinists I.A.S.1994


Pigeons, Birds, Dogs ASSISTANT GRADE, 1993

Directions (questions 14 to 20) in each of the following questions, choose the Venn diagram which bestillustrates the relationship among three given items HOTEL MANAGEMENT, 1991

14. Diseases, leprosy, scurvy

15. Hockey, cricket, games

16. Yak, zebra, bear

17. Animals, men, plants

18. Mercury, Mars, Planets

19. Sun, Moon, Stars


Tall men, Black haired people, Indians

Questions 21 to 29:

Directions: Choose the Venn diagram which best illustrates the three given classes in each question.

RAILWAYS-1990, C.B.I-1991

21. Protons, Electrons, Atoms

22. Sun, Planets, Earth

23. Dog, Animal, Pet

24. Science, Physics, Chemistry

25. Atmosphere, Hydrogen, Oxygen

26, Wheat, Grains, Maize

27. Machine, Lathe, Mathematics

28. Biology, Botany, Zoology

29. Citizen, Educated, Men

Directions (Questions 30 to 35): In each of the following questions, there are three words which are relatedin some way. The relationship in each case is indicated by one of the four alternative which best states therelationship is your answer. C.A.T.1997

(a) P includes part of Q and part of R but Q and R are independent of R.(b) P includes Q and part of R but Q is independent of R.(c) P, Q and R include part of one another.(d) P includes both Q and R.

30. Wheat, Loaf, Barley

31. Soldier, Army, Engineer

32. Singer, Writer, Actor

33. Researcher, Historian, Scholar

34. Wood, Steel, Furniture

35. Tiger, Elephant, Quadruped

(Questions 36 to 40).

Study the following figure and answer the questions given below.

36. How many doctors are neither artists nor players?

a.17 b.25 c.30 d.22

37. How many doctors are both players and artists?

a.4 b.3 c.8 d.30

38. How many artists are players?

a.22 b.17 c.25 d.4

39. How many artists are neither players nor doctors?

a.17 b.22 c.25 d.30

40. How many artists are neither players nor doctors?

a.17 b.25 c.30 d.22

(Questions 41 to 42).

In the following diagram rectangle represents men, Triangle represents educated, Circle represents urbanand square represents government employees I.A.S.1985

41. Which one of the following represents the educated men but not urban?

a.7 b.13 c.11 d.12

42. Which one of the following represents a woman who is urban as well as government employee?

a.10 b.13 c.14 d.11

(Questions 43 to 47)

Study the diagram given below and answer each of the following questions.

43. How many persons who take tea and wine but not coffee?

a.25 b.17 c.30 d.20

44. How many persons are there who take both tea and coffee but not wine?

a.7 b.15 c.30 d.20

45. How many persons take wine?

a.87 b.85 c.122 d.90

46. How many persons are there who takes only coffee?

a.55 b.45 c.35 d.50

47. How many persons takes all the three?

a.10 b.17 c.30 d.15

(Questions 48 to 50)

Study the following figure and answer the questions given below.

48. By which letter, the married teachers who live in joint family are represented?

a.Q b. R c. P d. S

49. By which letter, the married people who live in joint family but not are school teachers are represented?

a.Q b. T c. U d. S

50. By which neither letter, the people who live in joint family but are neither married nor teachers arerepresented?

a .A b. T c. U d. S

Directions (questions 51 to 55) the following five questions are based on the following diagram in whichthe triangle represents female graduates, small circle represents self-employed females and the big circlerepresents self-employed females with bank loan facility. Numbers are shown in the different sections ofthe diagram. On the basis of these numbers, answer the following: M.B.A.1997

51. How many female graduates are self-employed?

a.12 b.13 c.15 d.20

52. How many female graduates are not self-employed?

a.4 b.10 c.12 d.15

53. How many non-graduate females are self-employed?

a.9 b.11 c.12 d.21

54. How many self-employed female graduates are with bank loan facility?

a.5 b.7 c.12 d.20

55. How many non-graduate self-employed females are with bank loan facility?

a.3 b.8 c.9 d.12

56. Read the following figure and find the region representing persons who are educated and employed butnot conformed in job.

(a) a, c (b) a, b, c (c) b, d (d) a, b, c

Directions (questions 57 to 64); the following questions are based on the diagram given below:

I.A.S 1984

57. Who among the following is an educated male who is not an urban resident?

a.4 b.5 c.9 d.11

58. Who among the following is neither a civil servant nor educated but is urban?

a.2 b.3 c.6 d.10

59. Who among the following is a female, urban resident and also a civil servant?

a.6 b.7 c.10 d.13

60. Who among the following is an educated male who hails from urban area?

a.4 b.2 c.11 d.5

61. Who among the following is uneducated and also an urban male?

a.2 b.3 c.11 d.12

62. Who among the following is only a civil servant but not a male nor urban oriented and uneducated?

a.7 b.8 c.9 d.14

63. Who among the following is a male, urban oriented and also a civil servant but not educated?

a.2 b.3 c.6 d.10

64. Who among the following is a male civil servant, who is neither educated nor belongs to urban area?

a.7 b.13 c.4 d.1

65. From the following diagram identify the region which represents the students who study physics andmathematics but not chemistry? I.A.S.1995

a. t b. p + t + s c. v d. p +r +u

ANSWERS

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