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 $30$

Clearly $n(G\cap H)=42-12-5-7-8=10$

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

$=20+18-8=30$