Question

In a class of 50 students, each of the students passed either in mathematics or in science or in both. 10 students passed in both and 28 passed in science. Find how many students passed in mathematics?

Answer 1

Let $M=$ The set of students passed in Mathematics
$S=$ The set of students passed in Science
Then, $n\left(S\right)=28,n(M\cap S)=10,n(M\cup S)=50$
We have $n(M\cup S)=n\left(M\right)+n\left(S\right)-n(M\cap S)$
$50=n\left(M\right)+28-10$
$\Rightarrow n\left(M\right)=32$
Aliter
From the Venn diagram
$x+10+18=50$
$x=50-28=22$
Number of students passed in Mathematics $=x+10=22+10=32$