Question

Solve
If n(A) =15 , $n(A\cup B)=29$ , $n(A\sqcap B)=7$ find n(B) .

Answer 1

$n\left(A\right)=15$

$n(A\cup B)=29$ $n(A\cap B)=7$

$\Rightarrow n(A\cup B)=n\left(A\right)+n\left(B\right)-n(A\cap B)$

$\Rightarrow 29=15+n\left(B\right)-7$

$\Rightarrow n\left(B\right)=29-15+7=14+7=21$

$\therefore n\left(B\right)=21$