4MA1/2HR Jan 2023, Question 20: Three-Set Venn Diagrams
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2HR (Higher) · Calculator · 4 marks
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The question, in short
Use the eight given set sizes, including n(A ∩ B ∩ C) = 5 and n(C) = 14, to fill every region of a three-set Venn diagram with its number of elements.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 4 marks
- 1n(A ∩ B ∩ C) = 5 goes in the middle
- 2n(A ∩ B ∩ C′) = 2 is the A and B region outside C
- 3n(A ∩ C) = 5 and all 5 are in the middle, so A ∩ C outside B is 5 − 5 = 0
- 4n(A) = 17, so A only = 17 − 5 − 2 − 0 = 10
- 5n(B ∩ C) = 7 and 5 are in the middle, so B ∩ C outside A is 7 − 5 = 2
- 6n(A′ ∩ B ∩ C′) = 6 is B only
- 7n(C) = 14, so C only = 14 − 5 − 0 − 2 = 7
- 8n((A ∪ B ∪ C)′) = 3 goes outside all three circles
AnswerA only 10, A∩B only 2, B only 6, A∩C only 0, A∩B∩C 5, B∩C only 2, C only 7, outside 3
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