Type 1 (with the help of this formula solve the following questions)

Knowledge about the Venn-diagram

n (U) = n0(A) + n (AB) + n0(B) + n(A∪B)

n(A) = n0(A) + n(AB)

n(B) = n0(B) + n(AB)

Now,

n(A∪B) = n(A) + n(B) – n(AB)

∴ n(∪) = n(A∪B) + n(A∪B)

GRADE: X

SUBJECT: Maths

READING SECTION:

A B

only

A

only

B n(AB)

n(AB) n(A) n(B)

n(U)

TOPIC: SET

Workout Examples:

1. 50 students in a classroom like Mathematics or science or both. Out of them,

20 like both subjects, the ratio of number of students who like mathematics

to those who like science is 3:2, then;

a. Find the number of students who like Mathematics.

b. Find the number of students who like science only.

c. Show the above information in Venn-diagram

Solution:

Let M and S denote the sets of students who like Mathematics and science

respectively. Here, n(U) = n (M∪S) = 50

Let the common multiple be x. Then

n(M) = 3x

n(S)= 2x

n (M∩S) = 20

By using formula,

n(M∪S) = n(M) +n(S) - n(M∩S) or, 50=3x+2x-20

or, 50 = 5x-20 or, 5x=70

x=14

∴Number of students who like Mathematics = 3x = 3×14 = 42

a) n(m) = 3x

= 3 × 14

= 42

b) n0(s) = n(s) – n(m∩ 𝑠)

= 2× 14 − 20

= 28 – 20

= 8

2. In a survey of 100 people, it was found that 65 like folk songs, 55 like

modern songs and 35 liked folk as well as modern song:

Draw the Venn- diagram to illustrate the above fact.

How many people did not like both songs. Solution:

Let 'F' denote set of people who liked folk songs and 'M' denote set of people

who liked modern songs.

n(U) = 100 (Total number of people)

n(F) = 65 (who like folk songs)

n(M) = 55 (who like Modern songs)

n(F∪M) = x (say) (who don’t like both songs)

We know,

n(U) = n(F) +n(M) - n (F∩M)+n( F∪M )

or, 100 = 65+55-35+x

or, 100=85+x

0r, x = 100-85

or, x = 15

15 people don’t like both songs

Exercise

1. If A = {5, 7, 9, 11} and B = {5, 7, 13, 15}. Verify that

n(AB) = n(A) + n(B) – n(AB)

2. If n(AB) = 60, n(A) = 30, n(B) = 35, find n(AB)

3. In a group of 50 boys 30 drink tea, 20 drink coffee and 10 drink both.

Find how many boys drink none of these and present the above

information in venn-diagram.

4. In a group of 100 girls, 60 speak Nepali, 50 speak English and 10 speak

none of these languages. Find how many girls speak both languages and

present the above information in venn-diagram.

5. In a survey of related to choose place for educational tour among 200 \

students 60% students choosed Pokhara, 10% choosed Pokhara as well

as Gorkha, 20% students choosed neither of them,

i) Draw the Venn-diagram

ii) How many of them like only Pokhara?

iii) How many of them liked only one place?

6. In a group of 175 people, 90 people like rose, 50 of them like like rose

but not Jasmine, all of them like at least one flower. Find:

i) How many of them like both the flower?

ii) How many of them like Jasmine but not rose?

7. In a club of 65 players 10 players like football but not cricket and 20 of

them like cricket but not football. If 6 of them like both the game find.

i) How many of them like neither of game?

8. The question asked among 50 families, 23 families had Motorcycle, 17

families had Car and 18 did not have both. Find:

i) How many family had both the vehicles?

9. In a class there are 50 students, all of them like at least one of the tiffin

among MoMo and Chowmin, 20 students like both MoMo and

Chowmin. The ratioi of students who like MoMo and Chowmin is 3:2 find:

i) How many of them like MoMO?

ii) How many of them like Chowmin?

iii) Draw the Venn-diagram and illustriate the above information.

10. In a class of 50 students, 25 students like to play football, 35 like to play

cricket and 15 like to play both the games. How many students do not like

to play any games? Illustrate the above information by a Venn-diagram.

11. In a survey of a community, 45% of the people like Dashain festival, 65%

like Tihar festival and 20% like both festivals.

i) (Show it in Venn-diagram)

ii) (What percent of them do not like both?)

12. In a survey of 120 students, it was found that 17 drink neither tea nor

coffee, 88 drink tea and 26 drink coffee. By drawing a Venn-diagram, find

out the number of students who drink both tea and coffee.

13. Out of 100 students, 80 passed in Science, 71 in Mathematics, 10 failed in

both subjects and 7 did not appear in an examination. Find the number of

students who passed in both subjects by representing the above

information in a Venn-diagram.

14. In a group of 200 students who like game, 120 like cricket game and 105 like

football game. By drawing Venn-diagram, find:

i) how many students like both the games?

ii) how many students like only cricket?

15. In a class of 120 students, 95 like Account subject, 80 like Biology. If there

are none who don't like both subjects then:

i) Find the number of students who like Account only.

ii) Find the number of students who like Biology only.

iii) Show the above information in a Venn-diagram.

16. In a class of 60 students, 15 students liked Math only, 20 liked English

only and 5 did not liked any subject then:

i) Find the number of students to like both the subjects.

ii) Find the number of students to like at least one subject.

17. In a survey of 200 students, 30 liked neither to sing a song non to dance,

60 liked to to sing a song only and 50 liked to dance only then:

i) Illustrate these information in a Venn diagram.

ii) Find the total number of students who can sing a song.

18. In a survey of some students, it was found that 60% of the students studied

commerce and 40% studied science. If 40 students studied both the

subjects and 10% didn't study any of the subjects, by drawing a Venn-

diagram:

i) find the total number of students

ii) find the number of students who studied science only.

19. In a group of 95 students the ratio of student who like mathematics and

science is 4:5. If 10 of them like both the subjects and 15 of them like non

of the subjects then by drawing a Venn diagram find how many of them (a)

like only mathematics (b) like only science.

20. In a survey, it was found that the ratio of the people who liked modern songs and

folk songs is 8:9. Out of which, 50 people liked both songs, 40 liked folk songs

only and 80 liked none of the songs:

i) Represent above data in a Venn-diagram.

ii) Find the number of people who participated in the survey.

Note to the students:

1. Download the Online Home Assignment from Official School’s Webpage. (www.valleyview.edu.np) Click on Academic Menu and click downloads to get every grade Lockdown Assignment.

2. Please read the reading section carefully until you understand the given text.

3. Do or solve fairly the activity section in subject wise notebook.

4. Do not try to complete assignment in a hurry at once. Take time and accomplish sincerely and confidently.

5. After you complete your assignment, review, recall and test yourself.

6. The activity section will be corrected by your subject teacher after the school is reopened.

7. The best assignment will be rewarded.

8. If you have any query, please contact to the given contact person

Contact Person:

Name: Ram Prasad Dhungana

Phone No.: 9841315843

Email Address: rp.dhungana2011@gmail.com