Question

In the Venn diagram, the numbers represent the number of elements in the subsets. Given that $\xi =F\cup G\cup H$ and $n\left(\xi \right)=42$, find $n(G^{\prime }\cup H)$

• A. $18$
• B. $28$
• C. $30$
• D. $38$

Answer 1

The correct option is C $30$

$n\left(\xi \right)=42$

$n\left(G\right)=12,n\left(F\right)=17,n\left(H\right)=8$

$n(F\cap G)=5,n(G\cap H)=0,n(F\cap H)=0$

$n\left(G^{\prime }\right)=42-7-5=30$

$n\left(H\right)=8,n(G^{\prime }\cup H)=n\left(G^{\prime }\right)+n\left(H\right)-n(G^{\prime }\cap H)=30+8-8=30$