Chapter787

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Venn diagrams are pictorial way of represent the set of article.There are different regions which needs proper understandingfor solving problems based on given Venn diagrams.

TYPE- ICase - I:

Two articles:

P Q

IA IIAB IB

here I A represents only AIB represents only BIIAB represents A and B

For example : 1 23

– represents student passed in English

– represents student passed in Reasoning.1 – represents student passed in English only.

2 – represents student passed in Reasoning only3 – represents student passed in both English Reasoning

both.Case: - II Three articles

P Q

R

1 2

3

4

5

67

1 – represents P only2 – represents Q only3 – represents R only4 – represents Q and R (not P)5 – represents P and Q (not R)6 – represents P and R (not Q)7 – represents P, Q and R

Ex:– 1 2

3

4

5

67

Engineer Doctor

Farmer 1 ® Engineer 2 ® Doctor

3 ® Farmer 4 ® Doctor who is farmer also5 ® Engineer who is doctor also6 ® Engineer who is farmer also7 ® Person who is Engineer, doctor and farmer.

E XAMPLE 1. In the following venn diagram identify thenumber which denotes Doctor who know both swimming anddancing.

1 2

4

5

6

7

® swimmers

® doctors

® dancers

(a) 5 (b) 3(c) 4 (d) 6

Sol. (c) Area 4 which is common to and

represents the required condition.

VENN DIAGRAMS H

R

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TYPE – IINote 1- When one class of items is completely included in theanother class of item and is represented by the given diagram.

I

II

eg:- I – MangoII – Fruit

Here all mango are fruit.Note 2: If two classes of item are completely different from eachother but they all are completely included in third class then therelationship is represent of the diagram.

III

I II

eg: I – represent potatoII – represent onionIII – represent vegetable

Note 3 : If two group of items having some common relationshipand both of them are all included in third class then therelationship is represented by the diagram.

III

I II

Ex:-Brother, Father, Male.I ® Brother II ® Father III ® MaleSome Brother may be Father and all are male.

Note 4: When one class of item is completely included in another group while third is not related to both of them then such conditionare diagrammatically represented by

I

II

III

Ex:- Cricketer, player and farmer I – Cricketer II – Player III – Farmer All cricketers are players but farmers not.

Note 5 :- If three group of things are related to each other.

I II

III

Ex:- Graduate, Engineer and Doctor Graduate may be Engineer and Doctor.

Note 6: When two group of items are completely unrelated toeach other while they are partly related with third group of itemand is shown in.

I II III

Ex:- Cloth, Red, Flowers.Some cloth are Red and also some Flowers are red.

Note 7:- When group of items are completely different from eachother

I

III

II

Red, Yellow, Black These are all different colour.

E XAMPLE 2. Diagrammatic representation of the following:(1) Women, Doctors, Anchors(2) Tall men, Black haired people, Indians(3) Mars, Solar System, Universe(4) Girls, Boys, Students(5) Children, Men, WomenSol.(1) W

A

DD ® Doctor W Women®

A Anchors®

Some women are doctors and some are anchors. Amongthese women, some are both doctors and anchors.

(2) B

I

TT ® Tall menB Black haired people®

I Indians®

Some Indians are tall men. Some Indians have black hair.Among these Indians, some Indians are tall men with black hair.

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(3) USM U ® Universe

S Solar System®

M Mars®

Universe contains Solar System and Solar System containsMars.

(4) S

BG G ® GirlsB Boys®

S Students®

Girls and boys are students.

(5) C

MWC ® ChildrenW Women®

M Men®

Children, Women and Men are three different groups.

Some times venn diagram can be represented by different types of geometrical figures.

E XAMPLE 3. ‘Triangle’ represents young persons, ‘circle’represents uneducated persons and ‘rectangle’ representsemployed persons.

1

27

3

4

6

5

Give the answers of the following questions :

(1) Which region represents young, uneducated and employed persons?

(2) Which region represents educated, employed and young persons?

(3) Which region represents young, educated and unemployed persons?

(4) Which region represents young, uneducated andunemployed persons?

Sol.

(1) Region – 4, because this region is common to all three.

(2) Region – 2, because this region is common between young persons and employed persons but not with uneducated.

(3) Region – 1, because this region contains only young persons not a part of uneducated region and employedregion.

(4) Region – 3, because this region is common between young persons and uneducated per sons but not included inemployed region.

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1. Which one of the following Venn diagrams represents the best relationship between Snake, Lizard, Reptiles?

(a) (b)

(c) (d)

2. Which diagram correctly represents the relationship between Human beings, Teachers, Graduates?

(a) (b)

(c) (d)

3. Which of the following diagram represents the relationshipamong sun, moon and stars?

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

4. Which of the following diagram represents correctrelationship Judge, Thief, Criminal?

(a) (b)

(c) (d)

5. Which diagram correctly represent the relationship between politician, poets and women?

(a) (b)

(c) (d)

6. Which of the following four diagram represent correctlythe relationship between musician, instrumentalists,violinists?

(a) (b)

(c) (d)

7. Choose the diagram which represent the relationship amongthe following :- Capsules, Antibiotics, In jection.

(a) (b)

(c) (d)

8. Selects the figures which represents the relationship between athletes, football players and cricket-players.

(a) (b)

(c) (d)

9. Which of the following diagram represents the country,states and District?

(a) (b)

(c) (d)

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10. Which of the diagram represents the given statements:-Some of the players are tennis players, some tennis playersare hockey players. No Cricket player is a hockey players?

(a) (b)

(c) (d)

Directions (Qs. 11-20) : In each of these questions, three wordsare related in some way. The relationship among the words inquestion can best represents by one of the five diagram.

(a) (b)

(c) (d)

11. Cabinet, Home Minister, Minister.12. Professors, Researchers, Scientists.13. Men, Rodents, Living beings.14. Parents, Mothers, Fathers.15. Nitrogen, Ice, Air.16. Musicians, Singers, Women17. Elephants, Carnivore, Tiger.18. Rings, Ornaments, Diamond Rings.19. Indoor games, Chess, Table tennis.20. Fish, Herring, Animal living in water 21. Which one of the following diagrams represents the

relationship among Delhi, Lucknow, Uttar Pradesh?

(a) (b)

(c) (d)

22. Which one of the following diagrams represents the correctrelationship among day, week, year?

(a) (b)

(c) (d)

23. Which one of the following diagrams best depicts therelationship among Homan Society - Youth Club. PoliticalParty and Youths ?

(a) (b)

(c) (d)

24. Which one of the following diagramsre represent correctrelationship among pigeon, birds, dogs ?

(1) (2) (3) (4)(a) 1 (b) 2(c) 3 (d) 4

25. In the given figure in a garden, square represent the areawhere jackfruit trees are grown, circle represent mangotrees and triangle represent coconut trees. Which number represent the common area in which all types of trees aregrown.

9

87

23

1

5

(a) 4 (b) 3(c) 7 (d) 8

26. In the following venn diagram, Identify the politicians fromurban areas who are corrupt.

Rural people

Urban peoplePolitician

Corrupt people

1

2

3 45

7 8 9

1112

(a) 4 (b) 8(c) 9 (d) 10

27 In the following figure, the boys who are cricketer and sober are indicated by which number ?

10

67

Cricketer

Sober

Boys

8Girls 4

2 9

1

(a) 6 (b) 5(c) 4 (d) 2

28. Which are the numbers that makes their presence felt inonly one of the geometric figures.

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1

2

3

4

6

78 9

(a) 4, 6, 7 (b) 1, 2, 9(c) 3, 7, 9 (d) 2, 3, 8

29. In the following venn diagram identify the better whichdenotes players who are also doctors but not artist.

A

BC

D E

F

G

H

Player

Doctor

Artist(a) B + E (b) E(c) B (d) A

30. In the given figure, the circle represents boys, trianglerepresents players and square represents rurals. What

portion represents rural sports boys.

A

B C

D

E F(a) E (b) F(c) D (d) B

31.

a bcd

e

g

f

School children

Artist

SingersAbove diagram represents school children, artist andsingers. Study the diagram and identify the region. Whichrepresents those school children who are artists not singers.(a) a (b) b(c) f (d) e

32.1

2 3

45 6

7

8

910 11

– Girls

– Athletics – Boys

– DisciplinedThe boys who are athletic and are disciplined are indicated

by which numbers.(a) 1 (b) 4(c) 6 (d) 10

Directions (Qs. 33-39) : The following question are based onthe diagram given below.

6

7

8

9

10

11

12 13

144

5

3

Rectangle represents malesTriangle represents educatedCircle represents urbanSquare represents civil servants

33. Who among the following is an educated male who is notan urban resident?(a) 4 (b) 5(c) 11 (d) 9

34. Who among the following is neither a civil servant nor educated but is urban and not a male?(a) 2 (b) 3(c) 6 (d) 10

35. Who among the following is a female urban resident andalso a civil servant?(a) 6 (b) 7(c) 10 (d) 13

36. Who among the following is an educated male who hailsfrom urban?

(a) 4 (b) 7(c) 10 (d) 13

37. Who among the following is uneducated and also an urbanmale?(a) 2 (b) 3(c) 11 (d) 12

38. Who among the following is only a civil servant but neither a male or urban oriented and uneducated?(a) 7 (b) 8(c) 9 (d) 14

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39. Who among the following is a male urban oriented and alsoa civil servant but not educated?(a) 13 (b) 12(c) 6 (d) 10

Directions (Qs. 40-43) : In the figure below there are threeintersecting circles each represents certain section of peopledifferent region are marked a.g. Read the statement in each of thefollowing questions and choose the letter of the region whichcorrectly represent the statements.

Chinese Painter

Musicians

A B

C

a b

cd e

f

g

40. Chinese who are painters but not musicians?(a) b (b) c(c) d (d) g

41. Painter who are neither Chinese nor musician?(a) b (b) c(c) f (d) g

42. Chinese who are musicians but not painters?(a) d (b) c(c) b (d) a

43. Chinese who are painters as well as musicians?(a) a (b) b(c) c (d) d

Directions (Qs. 44-47) : Refer to the following Venndiagram :

16

12

920

1314

9

15

1813 16

19

GEOGRAPHY

HISTORY

MATHEMATICS

SCIENCE

18

44. The number of students who took any three of the abovesubjects was(a) 62 (b) 63(c) 64 (d) 66

45. The number of students in total, who took History or Mathematics or Science, was(a) 183 (b) 190

(c) 424 (d) 43046. The number of students who took both History andGeography among other subjects was(a) 62 (b) 63(c) 65 (d) 66

47. Which subject was taken by the largest number of students?(a) Mathematics (b) Science(c) Geography (d) History

48. Identify the diagram that best represents the relationshipamong classes given below :Food, Curd, Spoons

(a) (b)

(c) (d)

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1. (d) Snake is different from Lizard but both are reptiles.

Snake

Lizard

Reptiles

2. (a) Some teachers may be graduates and vice-versa allteachers and all graduates are human beings.

Teacher Graduate

Human being

3. (d) Sun is stars. Moon is a satellite.

Star

SunMoon

4. (c) Judge is different from both the thief and criminal.

JudgeThief

Crimi nal

5. (d) Some politician may be poets and vice-versa.Some politician may be women and vice-versa.

No poets can be women as women poets is called poetess.

Poets Politician Women

6. (a)

Instrumentalists

Violinists

Musicians

7. (c) Capsules are different from injection but both are usesas antibiotics.

8. (b) Some athletes may be football players and vice-versa.Some athletes may be cricket players and vice-versa.Some athletes may be both football players and cricket

players.Some cricket players may be football players and vice-versa.

9. (c)States

District Country

10. (c)

Cricket Tennis

Hockey

11. (b) Home minister is a minister, minister is part of cabinet.12. (a) Some professor may be scientist or researcher.13. (c) Men, Rodents are entirely differents, but both are living

beings.14. (c) Mother and Father are entirely different but both are

parents.15. (d) Nitrogen is air but ice is different.16. (a) All three items are partly related.17. (d) Tiger is a carnivore, while elephant is not.18. (b) Herring is type of fish, fish belongs to the class of

water animals.19. (b) All diamonds rings are rings, all rings are ornaments.

1 (d) 7 (c) 13 (c) 19 (b) 25 (b) 31 (b) 37 (d) 43 (c)2 (a) 8 (b) 14 (c) 20 (c) 26 (c) 32 (b) 38 (a) 44 (a)3 (d) 9 (c) 15 (d) 21 (c) 27 (d) 33 (c) 39 (c) 45 (a)4 (c) 10 (c) 16 (a) 22 (a) 28 (b) 34 (b) 40 (a) 46 (b)5 (d) 11 (b) 17 (d) 23 (b 29 (c) 35 (c) 41 (c) 47 (b)6 (a) 12 (a) 18 (b) 24 (a) 30 (c) 36 (a) 42 (a) 48 (d)

ANSWER KEY

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20. (c) Chess and table tennis are differents but both are indoor games.

21. (c)

Delhi is separate state while Lucknow is part of Uttar Pradesh.

22. (a) Year

Week

Day

23. (b) Political Party

Youth club

Youths

24. (a)

Birds

Pigeon Dogs

25. (b) 3 represents the area common to all types.

26. (c) Required area common to , , .

27. (d) Regioins1 2 4 6 7 8 9 10

PersonsBoys

Girls

Sober

Cricketer

®

¯´ ´ ´ ´ ´

´ ´ ´ ´ ´ ´

´ ´ ´ ´

´ ´ ´ ´d

WV

X

ü ü ü

ü ü

ü ü ü ü

ü ü ü ü

Region 2 presents the boys who are cricketer and sober.28. (b) 1 represent only Circle.

2 represent only Rectangle.9 represent only another Rectangle.

29. (c) Area common to and .

30. (c) Area common to , and

33. (c) Area common to and34. (b) circle only35. (c) Area not common to rectangle but common to square

and circle.36. (a) Area common to Rectangle, Circle, Triangle37. (d) Area common to Rectangle and Circle.38. (a) Only area of square.39. (c) Area common to rectangle, square and circle.40-43

Athletes Football players

Cricket players

40. (a) Required region is one which is common to circle Aand B.

41. (c) Area that contain only B.42. (a) Area common to A and C.43. (c) Common area of A, B and C44. (a) The required set of students is denoted by region

common to any three circle only\ Required number = (13 + 13 + 18 + 18) = 62.

45. (a) The required set of students is denoted by regionslying inside the circles representing History,Mathematics and Science. \ Required number = (9 +14 + 18 + 15 + 16 + 13 + 13 + 20 + 18 + 13 + 16 + 19) = 183.

46. (b) The required set of students is denoted by the regionscommon to the circles representing History andGeography.\

Required number = (20 + 13 + 12 + 18) = 63.47. (b) Number of students who took History= (16 + 12 + 18 + 20 + 18 + 14 + 13) = 111.

Number of students who took Geography= (9 + 16 + 13 + 20 + 13 + 12 + 18) = 101.

Number of students who took science= (19 + 15 + 18 + 20 + 18 + 16 + 13) = 119.

Number of students who took mathematics= (9 + 14 + 13 + 20 + 13 + 15 + 18) = 102.

48. (d)

Food

Curd Spoons

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