Question

Ex. In a survey of 100 students, the number of students studying the various languages wer
found to be : English only 18, English but not Hindi 23, English and German 8, English 26, Germa
48, German and Hindi 8, no language 24. Find the number of students who were studying (i) Hina
(ii) English and Hindi (iii) English, Hindi and German.
SOLUTION Let E, H and G be the sets of students studying English, Hindi and Germa
respectively
. Let U be the set of students surveyed i.e. the universal set.
In the above Venn diagram, let a,b,c,d, e, f and g denote the number of students in th
respective
regions.​

Answer 1

Step-by-step explanation:

Total students=100

Only English =18

English but not hindi=23

English & sanskrit=8

English =26, sanskrit−48

Sanskrit & Hindi =8

No language =24

from above diagram we can see that no. of students studying Hindi=10+5+3

=18

No. of students studying English and Hindi=3.

E-English, H-Hindi, S-Sanskrit

We have, 

Only English = a=18 

English but not hindi = a+d=23 

English & sanskrit = d+e=8 

English = a+b+d+e=26 

d+e+f+g=48 

 a+b+c+d+e+f+g=100−24=76

∴a=18,b=0,c=10,d=5,e=3,f=5 and g=35

n(H∩E)=b+e=3.