1. **Problem statement:** Find how many pupils wore only Pink based on the Venn diagram and given data. 2. **Understanding the problem:** The Venn diagram shows three sets: Lemon, Pink, and Blue with overlapping regions representing pupils wearing combinations of these colors. 3. **Given data:** - Only Pink: 20 (from question 1) - Pink and Blue: 32 (from question 2) - All three colors: 21 (from question 3) - Either Lemon, Pink, or Blue (union): 23 (from question 4) 4. **Formula for union of three sets:** $$|L \cup P \cup B| = |L| + |P| + |B| - |L \cap P| - |P \cap B| - |L \cap B| + |L \cap P \cap B|$$ 5. **Explanation:** - $|L|$, $|P|$, $|B|$ are the numbers of pupils wearing Lemon, Pink, and Blue respectively. - $|L \cap P|$, $|P \cap B|$, $|L \cap B|$ are the numbers wearing exactly two colors. - $|L \cap P \cap B|$ is the number wearing all three colors. 6. **From the diagram and questions:** - Only Pink = 20 - Pink and Blue (including all three) = 32 - All three = 21 7. **Calculate pupils who wore Pink and Blue but not Lemon:** $$|P \cap B| - |L \cap P \cap B| = 32 - 21 = 11$$ 8. **Calculate pupils who wore either Lemon, Pink, or Blue:** Given as 23. 9. **Since the union is 23, and all three colors are 21, this suggests the numbers in the diagram are symbolic or partial.** 10. **Final answer:** The number of pupils who wore only Pink is **20** as given.