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4024/12 Oct/Nov 2023, Question 23: Three-Set Venn Diagrams

Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 3 marks

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The question, in short

Complete a three-set Venn diagram for 40 shoppers buying hats, scarves and gloves using given region counts, then find n(S ∩ (H ∪ G)′).

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

Part (a) · 2 marks

Use the given counts and conditions to fill in all missing regions of the Venn diagram for the 40 people.

  1. 1H ∩ S ∩ G = 2
  2. 2Everyone with a hat and scarf also has gloves, so H ∩ S only = 0
  3. 3Exactly two items: 0 + 0 + S ∩ G only = 4, so S ∩ G only = 4
  4. 4G only = 40 − (3 + 10 + 0 + 0 + 2 + 4 + 5) = 16
  5. 5H ∩ S only 0, H ∩ S ∩ G 2, S ∩ G only 4, G only 16

AnswerH ∩ S only: 0 H ∩ S ∩ G: 2 S ∩ G only: 4 G only: 16 (given: H only 3, S only 10, H ∩ G only 0, outside 5)

Part (b) · 1 mark

Work out n(S ∩ (H ∪ G)′), the number in the region of S outside H and G.

  1. 1S ∩ (H ∪ G)′ = people in S but not in H or G = S only
  2. 2n = 10

Answer10

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Also searched as: 4024/12/O/N/23 · 4024_w23_qp_12 · 4024 w23 12 · question 23.
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