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4024/11 Oct/Nov 2023, Question 18: Three-Set Venn Diagrams

Cambridge O Level Mathematics 4024 · Paper 11 (Non-calculator) · Non-calculator · 4 marks

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The question, in short

Complete a three-set Venn diagram for 40 sports club members using given counts for running, cycling and sailing, then describe a shaded region in set notation.

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (a) · 3 marks

Fill in the Venn diagram regions for R, C and S using the seven given member counts and the total of 40.

  1. 1R ∩ C ∩ S = 22 − 6 − 9 − 5 = 2
  2. 2C only = 24 − 9 − 2 − 3 = 10
  3. 3S only = 14 − 5 − 2 − 3 = 4
  4. 4Outside = 40 − (6 + 9 + 5 + 2 + 10 + 3 + 4) = 40 − 39 = 1
  5. 5R only 6, R ∩ C only 9, C only 10, R ∩ S only 5, all three 2, C ∩ S only 3, S only 4, outside 1

AnswerR only: 6 R ∩ C only: 9 C only: 10 R ∩ S only: 5 R ∩ C ∩ S: 2 C ∩ S only: 3 S only: 4 Outside all circles: 1

Part (b) · 1 mark

Write set notation for the shaded region inside G and H but outside F.

  1. 1Shaded: in G and in H but not in F
  2. 2G ∩ H ∩ F′

AnswerG ∩ H ∩ F′

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Also searched as: 4024/11/O/N/23 · 4024_w23_qp_11 · 4024 w23 11 · question 18.
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