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Venn diagram illustrating the intersection of three sets: Red, Yellow, and Blue.

Venn diagram showing three overlapping circles labeled Red, Yellow, and Blue, with numbers in each section representing set intersections.

Venn diagram showing three overlapping circles labeled Red, Yellow, and Blue, with numbers in each section representing set intersections.

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Show Answer Key & Explanations Step-by-step solution for: Venn Diagram Union And Intersection - GCSE Maths


Based on the Venn diagram provided, the task is to find the total number of elements in the universal set (indicated by the symbol $\xi$). To do this, we sum the numbers in all distinct regions of the diagram.

1. Inside the Red circle only: 2
2. Inside the Red and Yellow overlap (not Blue): 5
3. Inside the Yellow circle only: 6
4. Inside the Red and Blue overlap (not Yellow): 2
5. Inside all three circles (center): 3
6. Inside the Yellow and Blue overlap (not Red): 2
7. Inside the Blue circle only: 4
8. Outside all circles: 4

Total = $2 + 5 + 6 + 2 + 3 + 2 + 4 + 4$
Total = $28$

Final Answer:
28
Parent Tip: Review the logic above to help your child master the concept of union and intersection worksheet.
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