LOGICAL VENN DIAGRAM
TYPE - 1
Here are a few different types of a Venn diagrams with their implification mede clear.
Suppose you are given a group of 3 items. Then,
1) If the items evidently belongs to three different groups, the Venn diagram representing it would be shown the diagram
Ex. Doctors, Engineers, Lawyers
These three items bear no relationship to each other so there represent by 3 disjoint figures as shown
2) if one item belongs to the class of the second and the second belongs to the class of 3rd, then the representation is in the form of three consecutive circles, as shown.
Ex: seconds, Minutes, Hours
Clearly, seconds are a part of minutes and minutes are a part of hours. So, the Venn diagram would be as shown with circle A representing Seconds, circle B representing minutes and circle C representing Hours.
3) If two separate items belong to the class of the third, they are represented by two disjoint circles inside a bigger circle as shown.
Ex: Table, Chair, Furniture
Clearly, table and chair are separate items but both are items of furniture. So, they would be represented as in the adjoining figure with circle A representing Table, circle B representing Chair and circle C representing Furniture.
4) If two items belongs to the class of the third such that some items of each of these groups are common in relationship, then they are represented by two intersecting circles enclosed within a bigger circle.
Ex: Males, Fathers, Brothers
Clearly, some father may be brothers and vice-versa. So, father's and brothers would be represented by two intersecting circles. Also both fathers and brothers are males. So, the diagrammatic representation would be shown with circle A representing Fathers, circle B representing Brothers, and circle C representing Males.
5) if two items are partly related to the third and are themselves independent of each other they are represented by three intersecting circles in a line.
Ex: Dogs, Pets, Cats
Clearly, some dogs and some cats are pets. But all the pets are not dogs are cats. Also dogs and cats are not related to each other. So, the given items would be represented as shown in figure with circle A representing Dogs, circle B representing Pets and circle C representings Cats .
6) If the three items are partly related to each other, they are represented as shown in the figure.
Ex: Clerks, Government Employees, Educated Persons
Clearly, some clerks maybe Government employees and some may be educated. Similarly, some Government employees may be clerks and some maybe educated. Also some educated persons maybe clerks and some maybe Government employees. So, the given items may be represented as shown in figure, with three intersecting circles denoting the three classes.
7) If one item belongs to the class of second while third items is entirely different from the two, then they may be represented by the adjoining diagram.
Ex: Engineers, Human Beings, Rats
Clearly, all engineers are human being. This would be represent by two concentric circles. But the class of rats is entirely different from these two. Thus, these items would be represented as shown in the figure, with circle A representing Engineers, circle B representing Human Beings and circle C representing Rats.
8) if one item belongs to the class of second and the third item is partly related to these two, they are represented as shown.
Ex: Females Mothers, Doctors
Clearly, all mothers are females. This would be represent by two concentric circlea. But, some females and some mothers can be doctors. So, the circle representing doctors would intersect each of the two concentric circles. Thus, the diagram becomes as shown with circle A representing Mothers, circle B representing Females and circle C representing Doctors.
9) if one item belongs to the class of second and the third item is partly related to the second, they are represented as shown figure.
Ex: Males, Fathers, Children
Clearly, all fathers are males. This would be represented by two concentric circles. But some males are children. But children cannot be fathers. Thus, the diagram becomes as shown with circle A representing Fathers, circle B representing Males and the circle C representing Children.
10) if two items are partly related to each other and the third item is entirely different from the two, they are represented as shown the diagram.
Ex: Professor, Author, Children
Clearly, some professor can be authors and vice-versa. This would be represented by two intersecting circles. But the class of children would be entirely different from these two. Thus, the Venn diagram would be as shown with circle A representing Professors, circle B representing Authors and circle C representing Children.
EXERCISE- 1
** Directions(questions 1 to 10)
Each of the questions below contains 3 elements. these three elements may or may not have some linkage. Each group of the elements may fit into one of the diagrams at (a), (b), (c), (d) and (e). You have to indicate groups of elements in each of the question fit into which of the diagrams given below. The letter indicating the diagram is the answer.
1) Vegetables, Potato, Cabbage
2) Table, Chair, Furniture
3) Week, Day, Year
4) Judge, Thief, Criminal
5) Husband, Wife, Family
6) Square, Rectangle, Polygon
7) Bus, Car, Vehicle
8) Anxiety, Intelligence, Strength
9) House, Bedroom, Bathroom
10) Mustered, Barley, Potato
** Directions (Question 11 to 20)
In the following questions, 3 classes are given. Out of the five figures that follow, you are indicate which figure will best represent the relationship amongst the three classes.
11) Elephants, Wolves, Animals
12) Metal, Iron, Chlorine
13) Mammals, Cows, Crows
14) Women, Mothers, Widows
15) Authors, Teachers Men
16) Kerala, Bihar, India
17) Automobiles, Cars, Motorcycles
18) Brick, House, Bridge
19) Tea, Coffee, Beverages
20) Boys, Students, Athletes
** Directions (Question 21 to 30)
Each of these questions below contains 3 groups of things. Choose from the following 5 lettered diagrams, the one that depicts the correct relationship among the groups of things in each questions.
21) Tennis fans, Cricket players, Students
22) Flowers, Clothes, White
23) Smokers, Lawyers, Non-smokers
24) Human beings, Teachers, Graduates
25) Males, Fathers, Daughters
26) Fathers, Uncles Men
27) Musicians, Men, Women
28) Whales, Fishes, Crocodiles
29) Anti-social elements, Pickpockets, Blackmailers
30) Tall men, Black haired people, Indians
** Directions (Questions 31 to 35):
Given below are five possible membership schemes. In each case, mark the one you feel appropriate description of the three listed items.
31) Apple, Golden apples, Fruits
32) Triangles, Scalene Triangles, Right angled Triangles
33) Words with no vowels, Words with one vowel, Words with 2 vowels
34) Words with no vowel, Words with at most one vowel, Words with at least two vowels
35) Names beginning with a vowel, Names beginning names beginning with E, Names beginning with either A or P
** 36) Which of the following sets is best represented in the given diagram?
A) Animals, Insects, Cockroaches
B) Animals, Males, Females and Hermaphrodites
C) States, Districts, Union territories
D) Country, States, Districts
** 37) In the Accounts Department of a company, there are some who are only chartered Accountants qualification. Besides these, there are others who hold Management Accountancy qualification. Some of these Management Accountants have also done either Chartered or Cost Accountancy or both. Which of the following figures represents these facts ?
** 38) In a class of 46 students, 18 played football , 17 played cricket including 6 who played football, 16 students played hockey including 4 who played cricket, but not football. 5 students played Carrom but no outdoor games. Which of the following figures represents these facts ?
** 39) Some of the cricket players are tennis players, some tennis players are hockey players, no cricket player is a hockey player.
Which of the following diagrams correctly represents the above statements ?
**40) In a dinner party both fish and meat were served. Some took only fish and some only meat. There were some vegetarians who did not accept either. The rest accepted both fish and meet. Which of the following logic diagrams correctly reflect this situation ?
** Directions (Questions 41 to 60)
In each of these questions, 3 words are related in some way. The relationship among the words in the questions can best be represented by one of the five diagrams (a),(b),(c),(d),(e) given below. Mark your answer accordingly.
41) Teachers, College, Student
42) Mother , Homosapiens, Woman
43) Iron, Lead, Nitrogen
44) Cabinet, Home Minister, Minister
45) Parrots, Birds, Mice
46) Professor, Researcher ,Scientist
47) Men , Rodents, Living beings
48) Parents, Mother, Father
49) English, Latin, Greek
50) Nitrogen, Ice, Air
51) Musicians, Singers, women
52) Elephant, Carnivorous, Tiger
53) Fish, Herring, Animals living in water
54) Hospital, Nurse, Patient
55) Rice, Mustard, Beetroot
56) Nose, Hand, Body
57) Rings, Ornaments, Diamond rings
58) Furniture, Tables, Books
59) Indoor Games, Chess, Table Tennis
**Directions (Questions 61 to 70)
Each of these questions below contents 3 groups of things. you are to choose from the following five diagrams, the one that depicts the correct relationship among the three groups of things in each question.
61) Carrot, Food, Vegetable
62) Tie, Shirt, Pantaloon
63) Shirt, Collar, Pocket
64) Petals, Bouquet, Flowers
65) Dogs, Pets, Cats
66) Brinjal, Meat, Vegetables
67) Rhombus, Quadrilaterals, polygons
68) Languages, French, German
69) Sun, Planets, Earth
70) Classroom, Blackboard,. School
** Directions (Questions 71 to 80)
Choose the Venn diagram which best illustrates the three given classes in each of the following questions:
71) Protons, Electrons, Atoms
72) Papers, Stationary, Ink
73) Dog, Animal, Pet
74) Science, Physics, Chemistry
75) Atmosphere, Hydrogen, Oxygen
76) Wheat, Grains, Maize
77) Dog, Carnivorous, Tiger
78) River, Canal, Perennial sources of water
79) Students of Law, Students of Science, Men
80) Vertebraes, Non -vertebraes, Living beings
Directions (Question 81 to 90):
Choose the Venn diagram which best illustrates the three given classes in each questions :
81) Machine, Lathe, Mathematic
82) Citizens, Educated, Men
83) Honesty, Intelligence, Aptitude
84) Sun, Moon, Stars
85) Animals, Men, Plants
86) Mercury, Mars, Planets
87) Yak, Zebra, Deer
88) Water, Atmosphere, Hydrogen
89) Diseases, Leprosy, Scurvy
90) Doctors, Lawyers , Professionals
** Directions (Questions 91 to 100):
Each one of the following questions consists of 3 items. Using the relationship between these items, match each question with the most reliable diagram. The letter denoting that diagram is your answer.
91) Plums, Tomatoes, Fruits
92) Engineer, Doctor , People
93) Sea, Island, Mountain
94) Elected house, M.P, M.L.A
95) Musicians, Instrumentalists, Violinists
96) Grams, Beans , Legumes
97) Mountains, Forests, Earth
98) Biology, Botany, Zoology
99) Factory, Machinery, Product
100) Trucks, Ship, Goods
** 101) If animals that live on land and the animals that live in water are represented by two big circles and animals that live both in water and on land are represented by a small circle, the combination of these three can be best represented as :
** Directions (Questions 102 to 105 )
Choose the Venn diagram which best illustrates the three given classes in each question:
102) Window, Room , Wall
103) State, Country, City
104) Copper, Paper, Wire
105) Teacher, Graduate, Player
** Directions (Questions 106 to 111):
In each of the following questionz, there are three words which are related in some way. The relationship in each case is indicated by one of the four alternatives (a),(b),(c),(d) given below. The alternative which best States the relationship is your answer.
a) P includes part of Q and part of R but Q and R are independent of each other.
b) P includes Q and a part of R but Q is independent of R.
c) P, Q and R includes parts of one another.
d) P includes both Q and R.
106) Wheat, Loaf, Barley
107) Singer, Writer, Actor
108) Soldier, Army, Engineer
108) Wood, Steel, Furniture
108) Teacher, Writer, Musician
109) Tiger, Elephant, Quadruped
** Directions (Questions 112 to 115)
Given below are five patterns represented by circles A, B and C which indicate the logical relationship between and among the respective to descriptions. On the basis of description given for A, B and C respectively in the questions, decide which of the given patterns (a),(b),(c),(d),(e) best illustrates the logical relationship.
112) A) Doctor B) Male C) Actor
113) Rose B) Flower C) Lotus
114) Father B) Mother C) Child
115) Gold B) Ornament C) Silver
***Directions (Questions 116 to 125):
Of the four alternatives in each of the following questions, three alternatives are such that the three words in each are related among themselves in one of the five ways represented by (a),(b),(c),(d) and (e) below while none of these relationships is applicable to the remaining alternative. That is your answer:
116) a) Army, General, Colonel
b) Boy , Students, Players
c) Painter, Scholar, Table
d)Man, Typist, Peon
117) a) Hen, Dog, Cat
b) Body, Ear, Mouth
c) Bed, Ward, Nurse
d) Tiger, Animal, carnivorous
118) a) Atmosphere, Air, Oxygen
b) Boy, Girl, tstudent
c) Man, Worker, Garden
d) Animal, Dog, Cat
119) a) Animal, Mammal, Cow
b) Colour, Cloth, Merchant
c) Colour, Red, Blue
d) Male, Horse, Mare
120) a) Metal, Sodium, Copper
b) Mammal, Nurse, Women
c) Cereal, Wheat, Rice
d) Males, Cousins, Nephews
121)a) Bed, Ward , Hospital
b) Girl , Athlete, Singer
c) Copper, Zink, Iron
d) Book, Page , Paragraph
122) a) Star, Moon, Mars
b) professor, scholars, politician
c) maid, doctor, woman
d) swimmer,. carpenter, politician
123) a) Periodical, weekly, book
b) mineral, copper, wood
c) doctors, human beings, married people
d) Army, Doctor, engineer
124)a) director, engineer , musician
b) apple, orange, mango
c) fruit, pear, grass
d) oxygen, air ,water
125) a) mineral, iron, copper
b) dean, painter, singer
c) seed, leaf, root
d) Piston, engine, wheel
Answers:
1B 2B 3A 4E 5B 6A 7B 8C 9B 10C 11C 12B 13B 14D 15A 16C 17C 18E 19C 20A 21C 22A 23A 24E 25D 26D 27A 28B 29E 30C 31A 32E 33D 34C 35B 36C 37C 38C 39C 40A 41C 42B 43E 44B 45D 46A 47C 48C 49E 50D 51A 52D 53B 54C 55E 56C 57B 58D 59C 60B 61A 62C 63D 64A 65D 66E 67A 68D 69E 70A 71B 72B 73C 74B 75B 76B 77B 78A 79E 80B 81A 82B 83C 84A 85A 86E 87C 88D 89E 90E 91E 92B 93E 94B 95A 96B 97C 98B 99B 100D 101B 102B 103A 104D 105C 106A 107C 108A 109A 110C 111D 112A 113B 114C 115A 116C 117A 118C 119B 120D 121C 122A 123C 124B 125C
TYPE -2
EXERCISE -1
1) Which number is an all the geometrical figure ?
A) 3 B) 4 C) 5 D) 8
2) Study the figure given below carefully and answer the questions that follow:
1) Which number belongs to all the figures ?
A) 3 B) 4 C) 6 D) none
2) What is the sum of the numbers which belong to two figures only ?
A) 6 B) 15 C) 20 D) none
3) What is the product of the numbers which belongs to three figures only ?
A) 27 B) 162 C) 648 D) none
4) What is the sum of the numbers which belong to one figure only ?
A) 5 B) 16 C) 21 D) none
5) What is the products of the numbers which belong to two figures only?
A) 64 B) 192 C) 384 D) none
3) In the following diagram, 3 classes of population are represented by three figures. The triangle represents the school teachers, the square represents the married persons and the circle represents the person living in joint families.
1) Married persons living in joint families but not working at school teachers are represented by
A) C B) F C) D D) A
2) Persons who live in joint families, are unmarried and who do not work as school teachers are represented by
A) C B) B C) E D) D
3) Married teachers living in joint families are represented by
A) C B) B C) D D) A
4) School teachers who are married but do not live in joint families are represented by
A) C B) F C) A D) D
5) School teachers who are neither married nor do live in joint families are represented by
A) F B) C B) B D) A
** 4) In the following diagram, the square represents, the circle 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 girls who are swimmers but don't play tennis ?
A) C B) D C) G D) H
2) Which letter represents girls who are swimmers, play tennis but are not tall ?
A) B B) E C) F D) none
3) Which letter represents tall girls who do not play tennis and are not swimmers?
A) C B) D C) E D) G
4) Which letter represents tall persons who are gents and swimmers but do not play tennis ?
A) I B) J C) K D) L
5) The following questions are based on the diagram given below:
1) The rectangle represents Government employees.
2) The triangle represents urban people.
3) The circle represents graduates.
4) The square represents clerks.
1) Which of the following statements is true ?
A) All Government employees are clerks.
B) Some government employees are graduates as well as clerks.
C) All Government employees are graduates.
D) All clerks are Government employees but not graduates.
2) Which of the following statement is true ?
A) All urban people are graduates.
B) Some clerks are Government employees but not urban.
C) All Government employees are clerks.
D) Some urban people are not graduates
3) Choose the correct statement:
A) Some clerks are Government employees.
B) No clerk is urban.
C) All graduates are urban.
D) All graduates are Government employees.
Exercise-2
1) Which of the following statements is correct with regard to the given figure ?
A) A and B are in all the three shapes.
B) E, A, B, C are in all the three shapes.
C) F, C, D, B, A are in all the three shapes.
D) only B is in all the three shapes.
2) Which number is in the square, ellipse and triangle ?
A)1 B) 5 C) 6 D) 7
** Directions (Questions 3 to 5)
Study the following diagram to answer these questions:
3) Find out the number that lies inside all the figures:
A) 2 B) 5 C) 9 D) none
4) What are the number that lie inside any two figures?
A) 2,1 B) 5,1 C) 5,9 D) 9,1
5) Find out the number that lies only inside the triangle:
A) 1 B) 2 C) 5 D) 9
** Directions (Questions 6 to 9):
These questions are based on the diagram given below :
6) Which number is inside all the three figures?
A) 2 B) 6 C) 7 D) 8
7) What is the sum of the numbers which belong to two figures only?
A) 10 B) 14 C) 18 D) none
8) Multiply the number which belongs to the square only with the sum of the numbers which belong to the trapezium only. What is the result ?
A) 45 B) 60 C) 75 D) none
9) Multiply the number which belongs to all the three figures with the sum of the numbers which belong to the triangle only. What is the result ?
A) 14 B) 35 C) 49 D) none
10) Study the diagram below and identify the region representing youth who are employed but not educated.
A) 4 only B) 5,6 C) 1,4,7 D) 4,7
*** Directions ( Questions 11 to 14):
In the figure given below, there are three intersecting circles each representing certain section of people. Different regions are marked a---- g. Read the statements in each of the following questions and choose the letter of the region which correctly represents the statement.
11) Chinese who are painters but not musicians:
A) b B) c C) d D) g
12) Painters who are neither Chinese nor musicians:
A) b B) c C) f D) g
13) Chinese who are musician but not painters
A) d B) c C) b D) a
14) Chinese who are Painters as well as Musicians
A) a B) b C) c D) d
** Directions: (Questions 15 to 19):
Study the following figure carefully and answer the given questions:
15) Which region denotes Indian leaders who are not singers
A) 2 B) 3 C) 4 D) 5
16) Which region represents Indian lenders who are singers ?
A) 2 B) 3 C) 4 D) 5
17) Which region represents leaders who are neither singers nor Indians?
A) 2 B) 3 C) 6 D) 7
18) which region represents Indian singers who are not leaders ?
A) 1 B) 2 C) 3 D) 4
19) Which region represents singers who are neither Indians nor leaders?
A) 2 B) 4 C) 6 D) 7
** Directions(Questions 20 to 24):
In the following diagram, the circle represents College Professors, the triangle stands for Surgical Specialists, and Medical Specialists are represented by the rectangle.
20) College professors who are also surgical specialists are represented by
A) A B) B C) C D) D
21) Surgical Specialists who are also Medical Specialists but not Professors are represented by
A) B B) C C) X D) Z
22) C represents
A) Medical Specialists
B) College Professors
C) Surgical Specialists
D) Medical and Surgical Specialists
23) B represents
A) Professors who are neither Medical nor Surgical Specialists.
B) Professors were not Surgical Specialists
C) Medical Specialists who are neither Professor nor Surgical Specialists
D) Professors who are not Medical Specialists.
24) College Professors who are also Medical Specialists are represented by
A) A B) X C) Y D) Z
** Directions (Question 25 to 28):
Study the diagram given below to answer these questions :
The triangle in the above figure depicts women in villages, the square depicts the unemployed women and the circle depicts the educated women.
25) Educated employed women in villages are represented by
A) D B) E C) F D) G
26) What does letter D represent ?
a) uneducated women in villages
b) unemployed women in villages who are not educated.
c) educated unemployed women
d) educated employed women
27) Educated unemployed women in villages are represented by
A) A B) B C) D D) E
28) Educated unemployed women are represented by
A) B and C B) D and E C) E and F D) G and E
** Directions (Questions 29 to 33) :
In the following questions, answers are to be based on the diagram given below, where the Triangles represent doctors, the circles represents players and the rectangle represents artists.
29) Which numbered space in the diagram represents doctors who are also players in artists ?
A) 2 B) 3 C) 4 D) 5
30) Which number represents artist who are also players only ?
A) 4 B) 6 C) 7 D) 8
31) Which number represents artists who are neither players nor doctors ?
A) 1 B) 2 C) 3 D) 4
32) Which number represents doctors who are neither players nor artists?
A) 2 B) 3 C) 4 D) 5
33) Which number represent players who are neither artists nor doctors
A) 1,2 B) 3,4 C) 6,7 D) 7,8
34) In the following diagram, the square represents women, triangle represents corporate managers and circle represents MBAs. Which numbered part represents -- women -- MBA-- corporate managers ?
A) 3 B) 5 C) 8 D) 13
35) A result of a survey of 1000 persons with respect to their knowledge of Hindi(H), English(E) and Sanskrit(S) is given below:
What is the ratio of those know all the three languages to those who do not know Sanskrit ?
A) 1/9 B) 1/10 C) 10/17 D) 5/27
** In the following figure, the boys who are athletes and disciplined or indicated by which number ?
The triangle represents girls, the circle athletics, the rectangle boys and the square disciplined
A) 1 B) 2 C) 6 D) 10
*** 37) In the Venn diagram given below, circle represents sportspersons, square represents unmarried persons, triangle represents women and rectangle represents educated persons. Each section is numbered. Study this diagram to answer the following questions.
Which section are represented by the region numbered 11 ?
A) Married Educated Sportswomen
B) Unmarried uneducated women sports persons
C) Married educated sportsmen
D) Unmarried educated sportswomen
**Directions (Question 30 to 45):
The following questions are based on the diagram given below :
a) Rectangle represents males
b) Triangles represents educated
c) Circle represents urban
d) square represents civil servants
38) Who among the following is an educated male who is not an urban resident?
A) 4 B) 5 C) 9 D) 11
39) 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
40) Who among the following is a female , urban resident and also a Civil Servant ?
A) 6 B) 7 C) 10 D) 13
41) who among the following is an educated male who hails from urban area
A) 4 B) 2 C) 11 D) 5
42) Who among the following is uneducated and also an urban male?
A) 2 B) 3 C) 11 D) 12
43) 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
44) Who among the following is a male, urban oriented and also a civil servant but not educated
A) 13 B) 12 C) 6 D) 10
45) 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
** Directions (Question 46 to 50):
In the following figure, rectangle, square, circle, triangle represent the region of wheat, gram, maize and rice cultivation respectively. On the basis of the above figure, answer the following questions.
46) Which area is cultivated by all the four commodities ?
A) 7 B) 8 C) 9 D) 2
47) Which area is cultivated by wheat and maize only
A) 8 B) 6 C) 5 D) 4
48) Which area is cultivated by rice only
A) 5 B) 1 C) 2 D) 11
49) Which area is cultivated by maize only
A) 10 B) 2 C) 3 D) 4
50) Which area is cultivated by rice and maize and nothing else?
A) 9 B) 8 C) 2 D) 7
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