Question

$A$ and $B$ are two sets such that $A$ has $5$ elements, $B$ has $7$ element while $A\cap B$ has $3$ elements, then what will be the $n(A\cup B)$?

• A. $12$
• B. $9$
• C. $35$
• D. $2$

Answer 1

The correct option is B $9$

Given : $n\left(A\right)=5,$
$n\left(B\right)=7\text{and}$
$n(A\cap B)=3.$

We know,
$n(A\cup B)=n\left(A\right)+n\left(B\right)-n(A\cap B)$
Hence, $n(A\cup B)=5+7-3$
$=9$