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(1), (2), (3), , (), , British Mathematician John Venn used diagrams, , to represent groups, hence these are called Venn, diagrams., , The set of objects is called group. For e.g.-Cars,, , motorcycles, buses, trucks etc. come in a group of, , vehicles. All of them together will be called a group, , of vehicles whereas different vechicles are called, , elements of this group., , There is a total of three types of questions asked in, , this chapter:, , First we will learn to solve questions based on type-1., Type-1, , The relationships found in this, are based on real, , life. There will be two or more elements in the, , question and the relationship between them has to, , be represented by Venn-diagrams., , There are mainly three types of relations in the, different elements, which are represented using, Venn-diagram:, All, Some, No, , All, , This relation is represented using the following, diagram. In Venn-diagram the relation of, , "All" can be seen only from one side. For e.g.- Mango,, fruits + All mangoes are fruits. Hence, there is, relation of "All". But all fruits are not mangoes i.e., Some fruits are mangoes. Thus we found that relation, of "All" is from Mangoes to fruits whereas there is, relation of "Some" from Fruits to Mangoes. Because, the relation of "All" can be seen only from one side., , , , Therefore, whenever there is relation of "All" between, two or more elements from one side, we have to use, the Venn-diagram of "All"., , Let's understand the relation of "All" with the help, of following examples:, , Man, Brother: All brothers are men., , , , (2), (3), (4), (5), , Q), , (2), , (3), (4), , (1), (2), (3), (4), , (5), , Vehicle, Car: All cars are vechicles., , Chair, Furniture: All Chairs are furniture., Woman, Sister: All sisters are women., , Wife, Mother: All mothers are wives., , The relation of "All" can be shown on the basis, of Space. For e.g., India, Delhi: Delhi is in India. Hence there is, relation of "All" between both on the basis of space., , India, , Lukhnow, Uttar Pradesh: Lucknow is in Uttar, , Pradesh., , Class, Students: All students are in the class., , Hospital, Doctor: All doctors are in hospital., Some, , This relation can be represented using the following, diagram., , In Venn-diagram the relation of "Some" can be seen, from both sides. For e.g., Doctor, woman~ Some doctors are women and, some women are doctors. Hence, we found that the, relation of "Some" can be seen from both sides., , Therefore, whenever there is relation of "Some", between two or more elements from both sides, we, have to use the Venn-diagram of "Some"., , Let's understand the relation of "Some" with the, help of following examples:, , Teacher, Man: Some teachers are men and Some, men are teachers., , Students, Boys: Some students are boys and some, boys are students., , Engineer, Teacher: Some engineers are teachers, and some teachers are engineers., , Brother, Husband: Some brothers are husbands, and some husbands are brothers., , Singer, Dancer: Some singers are dancers and, some dancers are singers., , , , pane, PV PURTInamrner, , Scanned with CamScanner

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VE., , , , Note: (1) Except "Students" the relation of "Teacher" with, , Q), (2), (3), , (1), , (2), , (3), , all others will be "Some",, (2) The relation of "All" or "Some" between two or, more elements exists only when one element can, be called by the name of another element in this., For e.g.-in (Mango, Fruits), mangoes can be called, fruits and fruits can be called mangoes. Similarly, in (Woman, Doctor), women can be called doctors, and doctors can be called women., , NO, When one element cannot be called by the name of, another then there is no relation between such, elements. The relation of "No" can be shown using, the following diagram., , OO, , For e.g.- Chair, Table: There is no relation between, these two elements. The chair cannot be called table, and the table cannot be called chair., , Hence, when there is no relation between two or, more elements, we have to use the Venn-diagram, of "No". Let's understand it with the help of following, examples:, , Mango, Apple: No mango is apple and no apple is, mango., , Brother, Sister: No brother is sister and no sister, is brother., , Husband, wife: No husband is wife and no wife is, husband., , Similarly (4) Car, bus (5) Copy, Pen, , (6) Rajasthan, Punjab (7) Teacher, Student etc., We will get the following ten possible Venn-diagrams, among X,Y and Z on the basis of these three, , relations:, , (X > Y): All, (> Z):, (X > Z):, , 2B, , (X > Y): Some, (Y > Z): Some, (X > Z): Some, , §, , , , , , , , , , (4), , (5), , (6), , (7), , (8), , (9), , (10), , , , (X > Y): No, (Y > Z):No, (X > Z): No, , (X + Y): No, (Y > Z): All, (XK > 2): All, , CL, , Some, Some, , (X > Y):, > 2):, (X > Z): Ne, , (X > Y): All, vo aN,, , (X > Z): Ne, , (X > Y): All, , (Y > Z): Some, (X + Z):No, , (X > ¥): All, (Y — Z): Some, (X > Z): Some, , (X > Y): Some, , Qf seg va, (X > Z):All, (xX > oc, , (Y > Z):No, , (X + Z):No, , , , Scanned with CamScanner

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Bxl, Sol:, , which of the following Venn-diagrams correctly, represents the relationship among Cat,Dog,Pet?, , "OO, , c) 2S, , The elements given have the following relationship:, Cat and Dog + No, , Dog and Pet + Some, , Cat and pet + Some, , , , , , Ans (B), Directions (2-5): Here four diagrams (A),(B),(C), , and (D) are given. Three elements are given in each of, the questions (2 to 5). Choose the Venn-diagram that, pest illustrates the relationship among three given, elements., , (2), 3), (4), 6), , (3), , (4), , (A), , , , "00, O, , (C) (D), , , , India, Jaipur, Rajasthan, Women, Wives, Mothers, Pilot, Plane, Sky, Shirt, Tie, Pant, (2) The relationship among the given elements:, India and Jaipur — All, Jaipur and Rajasthan > All, India and Rajasthan All, India, Rajasthan, Jaipur, Ans (A), The relationship among the given elements:, Women and Wives—> All, Wives and Mothers—> All, Women and Mothers > All, , Women, , Wives, , Mothers Ans (A), , The relationship among the given elements:, Pilot and Plane —» All, , Plane and Sky — All, , Pilot and Sky— All, , , , VENN - DIAGRAM, , (5), , Plane, Pilot, Ans (A), The relationship among the given elements:, Shirt and Tie No, Tie and Pant No, Shirt and Pant No, , SIO, Ans (B), , Directions{6-12): Here four diagrams (A),(B),(C) and, , (D) are given. Three elements are given in each of the, questions (6 to 12) Choose the Venn-diagram that best, illustrates the relationship among three given elements., , (6), (7), (8), (9), (10), QQ.), (12), , (A), , , , «OO, O, , o®, Car, Bus, Plane, Sun, Earth, Moon, , Engineer, Teacher, Women, Husband, Wife, Family, Rain, Lake, Water, , Grain, Pulse, Wheat, Planet, Earth, Mars, , Sol:(6) There is no relation among Car, Bus and Plane., , (7), , (8), , Ans (C), , There is no relation among Sun, Earth and Moon., , 6, ia, , There is relation of "Some" among Engineers,, Teachers and Women., , Engineers: Teachers, , Women Ans (D), , , , Scanned with CamScanner

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Teer, , (9), , (10), , qy), , (12), , VENN - DIAGRAM, , The relationship among the given elements:, Husband and Wife — No, , Wife and Family + All, Husband and Family + All, , Family, , EDC), , The relationship among the given elements:, Rain and Lake -> No, , Lake and Water-> All, Rain and water—> All, , Ans (B), , Water, , ENG), , The relationship among the given elements:, Grain and Pulse All, , Pulse and Wheat No, , Grain and Wheat > All, , 6, Ans (B), , The relationship among the given elements:, Planet and Earth > All, , Earth and Mars > No, , Planet and Mars-— All, , Planet, 7 Ans (B), , Directions (13-17): Here five diagrams (A),(B),(C), , (D) and (E) are given. There are three elements in each, of the questions (13 to 17). Choose the Venn-diagram, that best illustrates the relationship among the given, , elements., , °@D, OOD, , a) ©o, o@, ®), , , , (13), (14), (15), (16), (17), Sol:, , (14), , (15), , (16), , , , , , Sun, Stars, Moon, , Female, Mothers, Children, , Uncle, Rich People, Relatives, , Punjab, Chandigarh,Haryana, , Smokers, Men, Non-smokers, , (13) The relationship among the given elements., Sun and Star > All :, Star and Moon > No, , Sun and Moon -» No, , The relationship among the given elements:, Female and Mothers > All, , Mothers and Children > No, , Female and Children > Some, , Ans (A), , Female, , G&S, Ans (B), , The relationship among the given elements:, Uncle and Rich people + Some, , Rich people and Relatives» Some, , Uncle and Relatives —> All, , Relatives, , S) =, , Both Punjab and Haryana are different states and, Chandigarh is the capital of both states. There is, no perfect option available among the given options., So we have to choose that Venn-diagram which best, represents the relationship among these three., , Rich, People, , Chandigarh, , Punjab i Haryana, Ans (D), , Although the following Venn-diagram is perfect t0, show the relationship among Punjab, Chandigarh, and Haryana., , Chandigarh, , , , Scanned with CamScanner

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(7), , @), , There is no relation between smokers and nonsmokers. But some Smokers are Men. Similarly, gome Non-smokers are Men., , No perfect Venn-diagram can be made to show the, relationship among these three. So we have to, choose the best option among the given options., , Ans (D), , Directions (18-22): Here five diagrams (A),(B),(C),, , and (E) are given. There are three elements in each, of the questions (18 to 22). Choose the Venn-diagram, , that, , pest illustrates the relationship among the given, , elements., , (18), (19), (20), (21), (22), Sol:, , (19), , (20), , w QO), a ©o, 6), , Uttar Pradesh, Lucknow, Madhya Pradesh, Judge, Thief, Criminal, , Class, Teacher, Student, , Brothers, Hushand, Man, , Female, Sister, Engineer, , (18) The relationship among the given elements:, , Lucknow is in Uttar Pradesh while both Uttar, Pradesh and Madhya Pradesh are different states., , Uttar Pradesh, Lucknow, Madhya’, Pradesh,, Ans (C), , The relationship among the given elements:, Judge and Thief > No, , Thief and Criminal > All, , Judge and Criminal No, , ©), ©) Ans (C), , The relationship among the given elements:, Class and Teachers > All, , Teacher and Student > No, , Class and Student All, , (B), oD, , Student, , Drees, , Ans (B), , VENN - DIAGRAM €£$? _, , (21) The relationship among the given elements:, Brother and Husband + Some, Husband and Men- All, , Brother and Men All, , Brother (Ae~\, , The relationship among the given elements:, Female and Sister + All, , Sister and Engineer + Some, , Female and Engineer + Some, , Husband, Ans (E), , (22), , Female, , Directions(23-28): Here five diagrams (A),(B),(C),, (D) and (E) are given. There are three elements in each, of the questions (23 to 28). Choose the Venn-diagram, that best illustrates the relationship among the given, , (a) ; oe eCQG), , (C) ®, ®©o, , Ans (D), , , , (23) Teacher, Male, Female, (24) Bus, Train, Car, (25) Rhombus, Quadrilateral, Polygon, (26) Doctor, Teacher, Engineer, (27) Tennis Fans, Cricket Players, Students, (28) Pigeons, Birds, Dogs, Sol: (23) The relationship among the given elements:, Teacher and Male» Some, Male and Female > No, Teacher and Female > Some, Soo, Ans (B), (24) There is no relation among Bus, Train and Car., , Ans (A), , , , Scanned with CamScanner