Given the set $Z = \{\text{even numbers less than 19}\}$: - $A = \{6, 12, 18\}$ - $B = \{2, 6, 14, 18\}$ Complete the Venn diagram for this information. - Edexcel - GCSE Maths - Question 3 - 2021 - Paper 1

To fill in the Venn diagram, we first identify the elements in sets $A$ and $B$ and then place them into the correct regions:

1. Identify the sets:

   • Set $Z$ includes all even numbers less than 19: $\{2, 4, 6, 8, 10, 12, 14, 16, 18\}$.
   • Set $A = \{6, 12, 18\}$.
   • Set $B = \{2, 6, 14, 18\}$.

2. Determine the intersections:

   • The number $6$ is common in both $A$ and $B$, so it goes in the intersection of the two circles.
   • The number $18$ belongs to set $A$, but it's not in $B$, so it goes in the part of set $A$ outside of the intersection.
   • The number $2$ belongs to set $B$ but not to $A$, so it goes in the part of set $B$ outside of the intersection, while $14$ is also unique to $B$.

3. Fill the diagram:

   • Set $A$ will include the elements $\{6, 12, 18\}$: $6$ in the intersection, $12$ solely in $A$, and $18$ also in the intersection.
   • Set $B$ will contain $\{2, 6, 14, 18\}$: where $6$ is overlapped, $2$ and $14$ are exclusively placed in set $B$.

The Venn diagram will look like this:

• In the part of circle $A$ where only $A$ is present: $12$
• In the intersection of sets $A$ and $B$: $6$
• In the part of circle $B$ where only $B$ is present: $2$, $14$

4. Final Venn Diagram:
   • The completed diagram represents:
     • Circle $A$ (left) contains $\{12, 18\}$ in the non-overlapping part and $6$ in the overlap.
     • Circle $B$ (right) includes $\{2, 14\}$ in the non-overlapping part with $6$ being shared.