Question

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 at least one language?

Answer 1

The number of the  students  know at least one language is 135.

Step-by-step explanation:

Given:

80 number of  students know English.

60 number of  students know French.

50 number of students  know German.

30 number of students  know English and French.

20 number of students know French and German.

15 number of  students know English and German.

10 number of  students know all the three languages.

To Find:

The number of students  know at least one language.

Solution:

Let E = { set of students who know English}

Let F = { set of students who know French }

Let G={ set of students who know German }

As  given

Number of students know English  $n( E) =80$

Number of students know French $n( F) =60$

Number of students know German $n( G) =50$

Number of students know English and French $n( E\cap F) =30$

Number of students know French and German $n( F\cap G) =20$  

Number of students know English and  German $n( E\cap G) =15$

Number of students know all three language  $n( E\cap F\cap G) =10$

The number of students  know at least one language $=n(E)+n(F)+n(G)-n( E\cap F) -n( F\cap G) -n( E\cap G) +n( E\cap F\cap G)$

$= 80+60+50-30-20-15+10\\=135$                                                                          

Thus, the number of the students  know at least one language is 135.

Answer 2

135 students know at least one language.

Given,

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.

To find,

How many students know at least one language?

Solution,

Number of students who know English = 80

Number of students who know French = 60

Number of students who know German = 50

Number of students who know English and French = 30

Number of students who know French and German = 20

Number of students who know English and  German = 15

Number of students who know all three language  = 10

The number of students who know at least one language = 80 + 60 + 50 - 30 - 20 - 15 + 10 = 135

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