Question

If $A$ & $B$ are two sets such that $n\left(A\times B\right)=60$ & $n\left(A\right)=12$ also $n\left(A\cap B\right)=K$ , then the sum of maximum & minimum possible value of $K$ is

• A. $17$
• B. $12$
• C. $5$
• D. $7$

Answer 1

Answer: (C)

$n\left(B\right)=\frac{n\left(A\times B\right)}{n\left(A\right)}=5$
$\therefore$ $n\left(A\cap B\right)$ has minimum value $=0$
and $n\left(A\cap B\right)$ has maximum value $=n\left(B\right)=5$