Complement Intersection 7D643F

1. **State the problem:** We are given a Venn diagram with two sets $F$ and $G$ inside a universal set $\xi$. The numbers represent the counts of elements in different regions: - $12$ in $F$ only - $3$ in $F \cap G$ - $8$ in $G$ only - $7$ outside both $F$ and $G$ We need to find $n(F' \cap G')$, the number of elements outside both $F$ and $G$. 2. **Recall the definition:** - $F'$ is the complement of $F$, meaning elements not in $F$. - $G'$ is the complement of $G$, meaning elements not in $G$. - $F' \cap G'$ is the set of elements not in $F$ and not in $G$. 3. **Identify the region:** From the diagram, the number outside both $F$ and $G$ is given as $7$. 4. **Conclusion:** Therefore, $n(F' \cap G') = 7$. This is the count of elements outside both sets $F$ and $G$.