Question

12. In a language survey of students, it is found that 80 students know English, 60 know

French, 50 know German, 30 know English and French, 20 know French and German,

15 know English and German and 10 students know all the three languages. How many

students know i) at least one language ii) English only iii) French and one but not both

out of English and German iv) at least two languages​

Answer 1

Step-by-step explanation:

the explanation is given above

Answer 2

Given :  a language survey of students,

To Find  : How many students know

i) at least one language

ii) English only

iii) French and one but not both  out of English and German

iv) at least two languages​

Solution:

n(E)  = 80

N (F)  = 60

n(G) = 50

n ( E ∩ F) = 30

n ( F ∩ G) = 20

n ( E ∩ G) = 15

n  ( E ∩  F ∩ G) = 10

at least one language = n(E)  + N (F)   + n(G) - { n ( E ∩ F) + n ( F ∩ G) + n ( E ∩ G)} +  n  ( E ∩  F ∩ G)

= 80 + 60 + 50 - ( 30 + 20 + 15) + 10

= 190 - 65 + 10

= 135

135 knows atleast one language

English only =  n(E) -  n ( E ∩ F) - n ( E ∩ G)  + n  ( E ∩  F ∩ G)

= 80  - 30 - 15 + 10

= 45

at least two languages​

n ( E ∩ F) +  n ( F ∩ G) + n ( E ∩ G)- 2 n  ( E ∩  F ∩ G)  

30 + 20 + 15 - 2(10)

= 45

French and one but not both out of English and German

n  ( E ∩ F) + n ( F ∩ G)  - 2 n  ( E ∩  F ∩ G)

=  30 + 20  - 2 (10)

=  30

Learn More;

Venn diagram  Which of the option(s) is (are) correct?

brainly.in/question/21812746

Venn diagram  Which of the option(s) is (are) correct?

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