Logical Reasoning|| Chapter 2: Venn diagram statement base problems
📝 CHAPTER 2: VENN DIAGRAM STATEMENT BASED PROBLEM
📝Introduction: He Zirlai Venn Diagram statement based problem te hi Competitive exam na ah a pawimawh em em a, awlsam tak anga lang mahse mistake kan neih tam na a nih duh lawi si.. Competitive exam hrang hrang a pawimawh thin te lak khawm ani a Mizo leh english hman a ni bawk.Heng a hnuai ah hian hrilhfiahna pawimawh tak tak te ka dah tel bawk a, example ka lak ho pawh hi Question pawimawh tak tak lo chhuak tawh thin a ni e.Math leh Reasoning ah chuan eng tin nge kan solve ang tih ngaihtuah thiam hi a pawimawh em em a heng question ka lo solve sa te hi hna exam ah a chhuak ngei ngei dawn tihna lam ni lovin he mi chapter atanga problem awm thei tlangpui in zirtirna zawk a ni e.
— Elisa Lalrinngheta(Zo Guide)
Statement-based Venn diagram-te hi thil hrang hrangte inlaichinna bihchian thiamna leh thil lem hmanga tarlan thiamna endik nan hman thin an ni.
He section-ah hian, zawhnate hi statements leh thil thleng thei (conditions) hrang hrang hmangin zawh a ni a, a Zirlai leh hna exam bei tur te chuan chung thilte chu chipchiar taka lo enfiahin a tul angin chhanna an pe tur a ni.
🕵🏻 Step kal dan lo en ho ila :
1.Identify Conditions (Thil thleng thei hriat hran):
Inlaichinnate chiang zawka hriat nan statements chhunga thil thleng thei (conditions) chi hrang hrangte chu hriat hran tum tur a ni.
2.Visual Representation (Lem hmanga tarlan):
Hriatthiamna atan inlaichinnate chu lem (visual representation) hmangin siam tur a ni.
3.Analyze Relationships (Inlaichinnate bihchian):
Thil hrang hrangte lo inzawm dan chu hriat hran tawh sa (conditions) atang khan lo enfiah tur a ni.
🕵️✅ Understanding Visuals of Venn/Set representation:
🤷📝Venn Diagram Zawhnate Chinfel Dan Step-te:
1.Pawl/Set tinte hriatfiahna: Thuziak (statement)-a pawl emaw set hrang hrang tarlan te kha hriat hmasak tur a ni.
2.Set-te inzawmna enfiahna: Information min pek atang khan set hrang hrangte kha engtin nge an inzawm tih hriat tum tur a ni.
3.Venn Diagram rin luhna: Inzawmna kan hmuh chhuah tawh ang khan, bial (circle) emaw shape hrang hrang hmangin set-te chu tarlan tur a ni.
4.A hming vuahna: Circle ⭕ emaw shape kan rin hrang hrangte kha an pawl hming tura dik takin hming vuah vek tur a ni.
🕵🏻📝Tun ah chuan Example kan lo en ho tawh ang:
Q1.Kumthar lawmna ruai (party)-a sawm mi 600 zinga mi 250-in Indian ei tur an thlang a, mi 175-in Italian ei tur, tin mi 100-in Continental ei tur an ei a. Chubakah, mi 15-in Indian leh Italian ei tur an ei kawp a, mi 10-in Italian leh Continental ei tur an ei kawp a, mi 20-in Indian leh Continental ei tur an ei kawp bawk a ni. Mi pasarih (7)-in ei tur chi thum (3) te kha an ei vek a. Mi engzat nge he party-ah hian kal lo?
[ English version: Out of the 600 guests invited to the New Year's party, 250 opted for Indian food, 175 had Italian food, and 100 had Continental food. Additionally, 15 guests had both Indian and Italian food, 10 had both Italian and Continental food, and 20 had both Indian and Continental food. Seven guests had all three types of food. How many guests did not attend the party?]
Explanation:
Total guests invited = 600
Number of guests who had Indian food = 250
Number of guests who had Italian food = 175
Number of guests who had continental food = 100
Number of guests who had both Indian and Italian food = 15
Number of guests who had both Italian and Continental food = 10
Number of guests who had both Indian and Continental food = 20
Number of guests who had all three types of food = 7
Number of guests who had only Italian food = (175-15-7-10) = 143
Number of guests who had continental food = (100-20-7-10) = 63
Number of guests who did not attend ➡️ 600 – (208+143+63 + 10 +20 + 15 + 7)
➡️600-466 =134 Number of guests who did not attend.
[ Note: Competitive exam na ah chuan MCQ vekin a lo kal dawn oo]
Q2. Read the given information and answer the question asked by choosing the most appropriate option.
In a class of 75 students, everyone knows to play at least one of these two games, Cricket and Basketball. 41 people know how to play Basketball and 46 people know how to play Cricket.
In the class, how many people know how to play only one of the two games?
Explanation:
Total number of people = 75
Number of people who can play Cricket = 46
Number of people who can play Basketball = 41
Number of people who can play both = (46 +41) - 75 = 12
1.In-overlap-na lai fimkhur takin thliar hrang rawh: Venn diagram hmangin a in-overlap-na (in-finna) lai chiang takin lantir la, hmun tinte chu chhinchhiah vek rawh (entirnan: Indian chauh, Indian leh Italian, a pathum veka tel).
2.Symbol-te rualkhai takin hmang rawh: Symbol hman dante thuhmun rengin hmang rawh, hei hian inclusion-exclusion formula-a dah luh a ti-awlsam ang.
3.Chhiar nawn (overcounting) palh a awm em tih uluk takin en leh rawh: Inclusion-exclusion formula hian in-overlap-nate paih (subtract) leh a pathuma in-overlap belh leh (add back) hmangin a siamṭha ṭhin tih hre reng rawh.
4.Zawhna hman tam zualte lo zir hnem rawh: Zawhna pangngai (set pahnih emaw pathum nei) te hi zir hnem la, tichuan i tan a awlsam tawh hle ang.
✅Quick Recap Venn Diagram Tips leh Tricks:
1. Hriat tur pawimawh: Venn diagram hi set leh set inkar relationship tarlan nan hman a ni.
2. Set leh Element: Set hi circle hmanga tarlan a ni, element te chu circle chhunga dah a ni.
3. Intersection (∩): Set pahnih inkarah element an neih inang te.
4. Union (∪): Set pahnih element zawng zawng.
5. Difference (-): Set pakhat element, set dangin a neih loh te.
6. Complement ('): Set pakhat element ni lo, universal set-a element zawng zawng.
🕵️Tricks:
- Circle kha a pawimawh: Circle inkar overlap-na chu intersection a ni.
- Shaded area: Shaded area chu a tarlan set a ni.
- Element chhiar: Element te chu circle chhunga dah a ni.
- Venn diagram draw: Statement atanga draw a ni.
🤔Entirnan:
- A = {1, 2, 3}, B = {3, 4, 5}
- A ∩ B = {3}
- A ∪ B = {1, 2, 3, 4, 5}
I hriat duh emaw, zawhna i neih chuan min zawt rawh 😊
🕵🏻✅✍️📌Some Important Examples
Examples 1: This Venn diagram shows information about the number of people who have brown hair and the number of people who wear glasses.
A.10
B.15
C.11
D.4✅
🕵🏻Explanation: The intersection, where the Venn diagrams overlap, is the part of the Venn diagram which represents brown hair AND glasses. There are 4 people in the intersection.
🕵️Examples 2: Mary asks 40 people whether they own a cat or a dog. 17 people own a dog, 14 people own a cat and 7 people own a cat and a dog. Choose the correct representation of this information on a Venn diagram.
A.
B.
C.
D.
🕵🏻✅Correct Answer Option B.
Explanation: There are 7 people who own a cat and a dog. Therefore, there must be
7 more people who own a cat, to make a total of 14 who own a cat, and 10 more people who own a dog, to make a total of 17 who own a dog.
Once we put this information on the Venn diagram, we can see that there are
7+7+10=24 people who own a cat, a dog or both.
40−24=16, so there are 16 people who own neither.
🕵️Example 3. Some people were asked whether they like strawberry ice cream or chocolate ice cream. 82% said they like strawberry ice cream and 70% said they like chocolate ice cream. 4% said they like neither.
By putting this information onto a Venn diagram, find the percentage of people who like both strawberry and chocolate ice cream.
A.56% ✅
B.152%
C.12%
D.4%
✅ Solutions:
Example 4 : In a college, 200 students are randomly selected. 140 like tea, 120 like coffee and 80 like both tea and coffee.
1.How many students like only tea?
2.How many students like only coffee?
3.How many students like neither tea nor coffee?
4.How many students like only one of tea or coffee?
5.How many students like at least one of the beverages?
Solutions: The given information may be represented by the following Venn diagram, where T = tea and C = coffee.
Number of students who like only tea = 60
Number of students who like only coffee = 40
Number of students who like neither tea nor coffee = 20
Number of students who like only one of tea or coffee = 60 + 40 = 100
Number of students who like at least one of tea or coffee = n (only Tea) + n (only coffee) + n (both Tea & coffee) = 60 + 40 + 80 = 180
Example 5: In a survey of 500 students of a college, it was found that 49% liked watching football, 53% liked watching hockey and 62% liked watching basketball. Also, 27% liked watching football and hockey both, 29% liked watching basketball and hockey both and 28% liked watching football and basket ball both. 5% liked watching none of these games.
1.How many students like watching all the three games?
2.Find the ratio of number of students who like watching only football to those who like watching only hockey.
3.Find the number of students who like watching only one of the three given games.
4.Find the number of students who like watching at least two of the given games.
🕵🏻Solutions:
n(F) = percentage of students who like watching football = 49%
n(H) = percentage of students who like watching hockey = 53%
n(B)= percentage of students who like watching basketball = 62%
n ( F ∩ H) = 27% ; n (B ∩ H) = 29% ; n(F ∩ B) = 28%
Since 5% like watching none of the given games so, n (F ∪ H ∪ B) = 95%.
Now applying the basic formula,
95% = 49% + 53% + 62% -27% - 29% - 28% + n (F ∩ H ∩ B)
Solving, you get n (F ∩ H ∩ B) = 15%.
Now, make the Venn diagram as per the information given.
Note: All values in the Venn diagram are in percentage
Number of students who like watching all the three games = 15 % of 500 = 75.
Ratio of the number of students who like only football to those who like only hockey = (9% of 500)/(12% of 500) = 9/12 = 3:4.
The number of students who like watching only one of the three given games = (9% + 12% + 20%) of 500 = 205
The number of students who like watching at least two of the given games=(number of students who like watching only two of the games) +(number of students who like watching all the three games)= (12 + 13 + 14 + 15)% i.e. 54% of 500 = 270.
📝UPSC old Questions Solved
Q1. There are 100 students in a particular class. 60% students play cricket, 30% student play football and 10% students play both the games. What is the number of students who play neither cricket nor football? [CSAT 2011]
(a) 25
(b) 20
(c) 18
(d) 15
Solution:
Given that,
There are 100 students in a particular class.
60% students play cricket = 60
30% student play football = 30
10% students play both the games = 10
Now,
Let number of students playing cricket and football be C and F
Let p be the % of student playing neither cricket nor football
n(C∩F) = 10
n (C) = 60, n (F) = 30
So,
60 + 30 + p - 10 = 100
p = 20
🕵🏻Hence option (b) is correct
Q2. Out of 130 students appearing in an examination, 62 failed in English, 52 failed in Mathematics, whereas 24 failed in both English and Mathematics. The number of students who passed finally is [CSAT 2015]
(a) 40
(b) 50
(c) 55
(d) 6
Solution:
Given that,
Out of 130 students appearing in an examination, 62 failed in English, 52 failed in Mathematics, whereas 24 failed in both English and Mathematics.
Now,
Number of students failed in at least one subject = 62 + 52 - 24 = 90
Number of students passed = 130 - 90 = 40
Hence option (a) is correct
Q3. 19 boys turn out for playing hockey. Of these, 11 are wearing hockey shirts and 14 are wearing hockey pants. There are no boys without shirts and/or pants. What is the number of boys wearing full uniform? [CSAT 2018]
(a) 3
(b) 5
(c) 6
(d) 8
Solution:
Given that,
19 boys turn out for playing hockey.
11 are wearing hockey shirts
14 are wearing hockey pants.
There are no boys without shirts and/or pants.
Now,
Number of boys not wearing hockey shirt = 19 - 11 = 8
Boys wearing full uniform = 14 - 8 = 6 (No. of boys wearing hockey pants – No of boys not wearing hockey shirts)
🕵🏻Hence option (c) is correct
Q4. In a conference, out of a total 100 participants, 70 are Indians. If 60 of the total participants are vegetarian, then which of the following statements is/are correct? [CSAT 2019]
1. At least 30 Indian participants are vegetarian.
2. At least 10 Indian participants are non- vegetarian.
Select the correct answer using the codes given below:
(a) 1 only
(b) 2 only
(c) Both 1 and 2✅
(d) Neither 1 nor 2
Solution:
Given that,
In a conference, out of a total 100 participants, 70 are Indians.
60 of the total participants are vegetarian
Now,
Non vegetarians participants = 100 - 60 = 40
1. At least 30 Indian participants are vegetarian.
Considering 40 Indians to be non- vegetarians
Then vegetarians = 70 - 40 = 30
Hence statement 1 is correct
2. At least 10 Indian participants are non- vegetarian
Considering 60 vegetarians to be Indians
Non vegetarians = 70 - 60 = 10
Hence statement 2 is correct
Q5. In an examination, 80% of students passed in English, 70% of students passed in Hindi and 15% failed in both the subjects. What is the percentage of students who failed in only one subject? [CSAT 2024]
(a) 15%
(b) 20%
(c) 25%
(d) 35%
Solution:
Given that,
English = 80% student passed
Hindi = 70% students passed
Failed = 15% in both the subjects
Now,
Failed in English = 100 - 80 = 20%
Failed in Hindi = 100 - 70 = 30%
Failed in both the subjects = 15%
So,
Students Failed only in English = 20 - 15 = 5%
Students failed only in Hindi = 30 - 15 = 15%
Total students failed only in one subject = 15% + 5% = 20%
✅ Hence option (b) is correct
📝Practice Questions for MPSC ( Heng Question te hi a chhuak dawn tihna ani lova he lam hawi zawnga a lo chhuah palh chuan hetiang ang kan solved dan method hmang hian solved thin tur tihna ani mai zawk e)
Q 1. In a group of 100 students in Pachhunga University College, 60 study History, 50 study Geography, and 30 study both. How many students study neither History nor Geography?
A. 10
B. 20
C. 30
D. 40
Q2.Based on the statement "Some farmers are rich, and all rich people are investors," what can be concluded?
A. All investors are rich.
B. Some investors are farmers.
C. No farmers are investors.
D. All farmers are investors.
Question hi a update belh zel a ni dawn e......
Thankyou☺️.
