Question

In a class of $70$ students, $38$ students like physics, $21$ students like mathematics and $15$ students like both the subjects, then the number of students who like neither of the subjects is

• A. $27$
• B. $24$
• C. $11$
• D. $26$

Answer 1

The correct option is D $26$

Let $A$ and $B$ denote the number of students who like physics and mathematics respectively.
$\text{Then}n\left(A\right)=38,n\left(B\right)=21,n(A\cap B)=15$
$n(A^{\prime }\cap B^{\prime })=n(A\cup B{)}^{\prime }$
$=n\left(U\right)-n(A\cup B)$
where $U$ is the universal set.
$n(A^{\prime }\cap B^{\prime })=70-(38+21-15)$
$=26$