Question

$100$ students of class $12th$ opted for Mathematics while $90$ students opted for Biology. $170$ students opted for Mathematics or Biology. How much students opted for Mathematics and Biology?

• A. $360$
• B. $190$
• C. $20$
• D. None of the above

Answer 1

The correct option is C $20$

Let $A$be the set of students who opted Mathematics and $B$ be the set of students who opted Biology.

Given : $n\left(A\right)=100,n\left(B\right)=90,\text{and}n(A\cup B)=170$

We know that $n(A\cup B)=n\left(A\right)+n\left(B\right)-n(A\cap B)$
$\Rightarrow n(A\cap B)=n\left(A\right)+n\left(B\right)-n(A\cup B)$
Hence, $n(A\cap B)=100+90-170$
$=20$