class 10 sets

Set 1.1 7:02 AM

Tuesday, June 22, 2021

Important formulas

Important key word
out of, total ,survey =n(U)
either or , any of two =
as well as ,and ,both =

Neither nor ,antonym , opposite words =

we fill the Venn diagram from= intersection , only ,complement

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Q 2a if n(A) =35 and n(B) =30 and find the by drawing venn diagram

Solution
n(A) =35
n(B) =30

from venn diagram

3a) if P={ multiples of 2 up to 20} , Q={ multiples of 3 up to 24} and U= {integers from 1 to 25}
find by drawing venn diagram
solution
P={2,4,6,8,10,12,14,16,18,20}
Q={3,6,9,12,15,18,21,24}
U { , ,3, , ,6,7,8,9, , , , 3,… }

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Q4) in a set A and B A has 40 members and 50 members and 6 By how
draw a venn diagram .
many element for made ?

solution

n(A)= 40

n(B)=50

6

we have ,

6

69

3
so, 30 element for

Q 5a) if n(A)=40 , n(B) =60 and 8 find the value of

n(A)= 40 8
n(B)=60

we have ,

86
8

now filling Venn diagram

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Q 6) if A and B are two sub sets of universal set U in which n(U) =70 n(A) =40 , n(B)=20 and
then show it in a Venn diagram find the value of

solution
n(U) =70
n(A) =40 ,
n(B)=20

Filling in to Venn diagram

From the Venn diagram
76

Q 7a) In a survey of 60 people , 30 drinks mil , 25 drink curd and 10 students drink milk as well as
curd , draw Venn diagram find the students who drink neither of them
solution
Let M and C denote the set of students who drink Milk and curd respectively
n(U)= 60
n(M) = 30
n( C ) =25
Filling into Venn diagram

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from the venn diagram

we have
n(U) =
60=

Q 8 b) In a survey before an election 65% people liked leader A and 60% people liked leader B .If
15 % people did not like to open their opinion of any of the leader find the percentage of people
who liked both the leader by using Venn diagram

Solution :
Let A denote the set of people who like the leader A and B denotes the set of people who like the
leader B

n(A)=65
n(B)=60

from the Venn diagram
66

66
40=x

Q 9 a) In a group of 100 students, 68 like football game and 60 like Volleyball game . By drawing a
Venn diagram find
i) How many students like both games?
ii) How many students like only football?
iii) Show the above information on Venn diagram

solution
Let F and V denotes the sets of students who like the football or Volleyball respectively
n(U)= 100
n(F)=68
n(V)=60
n(

we have
n(U)=

set 2 Page 4

n(U)=

100=68+60-
Now , filling into Venn diagram

Q10 a) out of 90 civil servant , 65 were working in the office ,50 were working in the field and
35 were working in both the premises
i) how many civil servant were absent ?
ii) How many civil servant were working in the field only?
iii) Represent the above information in the Venn diagram ?
Solution
Let O and F denotes the set of workers who works in office and field respectively
n(U)=90
n(O)=65
n(F)=50

3

6 3
8

we have ,

98
98
we have

now representing on the Venn diagram

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Q 11 a) In an examination , it was found that 55% failed in math and 45% failed in English if
35% passed in both subjects
iv) What percentage failed in math only?
v) What percentage failed in English only?
vi) Represent the above the above information in a Venn diagram .
Solution
Let M and E denotes the sets of students who failed in the Math and English respectively
n(U) = 100
n(M)= 55
n( E) =45

3
we have
n(U) =

6
6

3

now representing in Venn diagram

Q12a) In an exam ,70% of the examination Passed in Science, 75% in the math and 10% failed
in the both subject .If 220 examination passed in both subjects , find the total number of

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in the both subject .If 220 examination passed in both subjects , find the total number of
students

solution
Let S and M denotes set of students who are passed in Science and math respectively
if n(U)=100
n(S)=70
n(M)=75

Now filling on the venn diagram

from Venn diagram

n(U)= 7 7

x=55

55% of total students study the both subjects

So,

total students=400

Q 13) In a class of 25 students , 12 have chosen Mathematics , 8 have choose Mathematics but
not Biology . If each of them has Chosen at least one, then find the numbers of students who
have chosen Mathematics and Biology and those who have chosen Biology but not Mathematics
solve by making a Venn diagram .
solution :
Let M and B denotes the sets of students wo has chosen the math and
n(U) =25

8

Now filling on the venn diagram

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from Venn diagram
n(U) = 8
25=12+x
x=13
So, 13
Q 14 ) out of 100 students of class V, 73 passed in mathematics and 84 in Nepali in the final
examination but 7 failed in both and 5 were absent in the examination . Find the number of
students who passed in the both subjects
solution
Let M and v denotes the sets of students …
n(U) = 100
n(M)= 73
n(N) = 84

7

now filling on Venn diagram

from the Venn diagram

n(U) = 8 73

100 =169-x

x=69

69

14b )

Out of 75 students in a class-x, 30 passed in mathematics and 40 in social

studies in the final examination but 10 failed in both subjects and 5 were absent

in the examination. Find the number of students who passed in both subjects.

Solution
Let M and S denotes the set of students in class X who passed in mathematics
and social respectively
n(U) =75

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n(U) =75
n(M) =30
n(S) =40

we have
n(U)=

75=
60 =

63
67

Q 15) out of 100 students in a class 20 student like math but not science and 30 students like
science but not math . If 20 students kike neither of both subjects
i) Show the above information in a Venn diagram
Ii) find the ratio of the students who like math to the student who like science
solution
Let
n(U) = 100

3

from the Venn diagram

n(U) = 3

3
n(M) =

The ration of students who like math to science =

Q15 b) 250 students in a group were asked whether they like mango apple . 80 students like
mango but not apple and 60 students like apple but not mango . If 50 students do not like both of
fruits then
i) Represent the above information in Venn diagram
ii) Find the ratio of the students who like to the students who like apple

Solution
Let
n(U)=

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n(U)=

from Venn diagram
n(U) =
Ex2

Q) 2a) If n(A) = 65 n(B) =50 n( C) = 40 , , ,
,,

solution

2b)

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2b)

We have

120=113+
Now representing on the venn diagram

3a)

3b)
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4a)

5b)

6a)

in an interview of 45 students , 12 liked mathematics and science , 5 liked mathematic and english ,
25 liked mathematics , 23 liked sciene , 4 liked all three subjects. 15 liked English , 10 liked and english .

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25 liked mathematics , 23 liked sciene , 4 liked all three subjects. 15 liked English , 10 liked and english .
How many students did not like any of the subjects ?
Solution , let M, S, E denote the sets of students who liked the Mathematics , Science, and English
respectively

3

we have ,

3

45
Now filling on Venn diagram

7a)

1) Ina vilage of 140 house , 60 believe in buddhiism, 70 in hindudism relion and 45 in other religion .
Among them 17 houses donot find any difference in Hindusim and buddism , 18 houses donot find any
difference in hinduism and other religion . 16 houdes donot find anny diffenence between buddhism
and other religion . If 16 houses donot believe in any religion find how many houses donot find any
diffenecce in any religion .show it in venn diagram
Solution ,
let B, H, O denote the set of houses which beieve in buddism Hinddudim , other relogion

6, 7, 6
7, 8

6,

we have,

6

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3

then draw Venn diagram
8a)

in a group of students , 20 study Account, 21 study Mathematics , 18 History , 7 study Account only . 10
study mathematics only , 6 study account and Mathematics only and 3 student Mathematics and
History only
i) How many students study all the subjects ?
ii) how many students are there altogether ?

Solution
Let A,M, H, denotes the sets of students who likes the account mathematics and history respectively

,7 8 6 3
From the Venn diagram ,

9a) use n(U)= 100

use
n(U)=

9a)

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q 10)

Q11

Solution

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Q 12

13a)
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13b) in a group of 60 people , 5 did not like any of tea , coffee and milk , if the ratio of people who like
only one , only two , and all three is 6:3:2 .find the numbers of people who like only one
Solution ,
Let T, C &M denotes the sets of students who like tea coffee ,milk respectively
ratio = 6:3:2
Number of people who like only one = 6x
Numbers of people who like only two =3
Numbers of people who like all three=

From Venn diagram
Number of people who like only one =

6

Numbers of people who like only two = b+d+f
3x=b+d+f
Numbers of people who like all three= e

it is

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