Question

In a survey of 100 students, the number of students studying the various languages were found to be: English only 18, English but not Hindi 23, English and Sanskrit 8, English 26, Sanskrit 48, Sanskrit and Hindi 8 ,no language 24. Find:

(ii) How many students were studying English and Hindi?

Answer 1

Let E,H and S be the sets of students who study English, Hindi, and Sanskrit, respectively. also,
let U be the universal set then,
Let, number of surveyed students =n(U)=100
Let, number of students studying English =n(E)=26
Let, number of students studying Sanskrit =n(S)=48
Let, number of students studying English and Sanskrit =n(E∩S)=8
Let, number of students studying English but not Hindi =(E∩H′)=23
Let, number of students studying Sanskrit and Hindi =n(S∩H)=8
Now, number of students studying Hindi and English are,
$\Rightarrow n\left(E\right)-n(E\cap H)=n(E\cap H^{\prime })$
$\Rightarrow 26-n(E\cap H)=23$
$\Rightarrow n(E\cap H)=3$
Therefore, the number of students studying English and Hindi is 3.