Question

There are $40$ students, $30$ of them passed in English $25$ of them passed in Maths and $15$ of them passed in both. Assuming that every students has passed at least in one subject. How many students passed in English only but not in Maths.

Answer 1

Let A and B be the sets of students who passed in English and Mathematics respectively, i.e., $n\left(A\right)=30$ and $n\left(B\right)=25$.

Also according to question,every student has passed at least in one subject.

Thus, total no. of students $=n(A\cup B)=40$

No. of student who passed in both English and Mathematics $=n(A\cap B)=15$

So, no. of students who passed in English only but not in Maths = $n(A-B)=n\left(A\right)-n(A\cap B)=30-15=15$.