Question

Solve the following question
If $n\left(A\right)=15,n(A\cup B)=29,n(A\cap B)=7$ then find $n\left(B\right)$=?

Answer 1

Given that,

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

$n(A\cup B)=29$

$n(A\cap B)=7$

$n\left(\right)=?$

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

$⟹29=15+n\left(B\right)-7$

$⟹n\left(B\right)=29-15+7$

$⟹n\left(B\right)=36-15$

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