Question

If $n\left(U\right)=60,n\left(A\right)=21,n\left(B\right)=43$ then the least and the greatest value of $n(A\cap B)$ are respectively ($U$ denotes universal set)

• A. $2,31$
• B. $3,36$
• C. $1,24$
• D. $4,21$

Answer 1

The correct option is D $4,21$

$n\left(U\right)=60,n\left(A\right)=21,n\left(B\right)=43$
Greatest value of $n(A\cap B)=n\left(A\right)=21$
$n(A\cup B)\le 60$
$\Rightarrow n\left(A\right)+n\left(B\right)-n(A\cap B)\le 60$
$\Rightarrow n(A\cap B)\ge 21+43-60=4$
Least value of $n(A\cap B)=4$
Hence, option 'D' is correct.