Question

If $n(A-B)=18$, $n(A\cup B)=70$, and $n(A\cap B)=25$ then find $n\left(B\right)$

Answer 1

Given:$n(A-B)=18$, $n(A\cup B)=70$, and $n(A\cap B)=25$

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

$\Rightarrow 70=18+25+n(B-A)$

$\Rightarrow 70=43+n(B-A)$

$\Rightarrow n(B-A)=70-43$

$\therefore n(B-A)=27$

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

$\therefore n\left(B\right)=25+27=52$