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0580/22 Oct/Nov 2023, Question 15: Venn Diagrams

Cambridge IGCSE Mathematics 0580 · Paper 22 (Extended) · Calculator · 3 marks

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The question, in short

Venn diagram work: shade a set region for P and Q, then use given counts to fill in all four regions for sets A and B.

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

Part (a) · 1 mark

Shade the area representing P union with the complement of Q on the two-circle Venn diagram.

  1. 1P ∪ Q′ is everything in P together with everything outside Q
  2. 2Shade every region except the part of Q outside P (Q only)

AnswerShaded: every region except Q only (P, and everything outside Q)

Part (b) · 2 marks

Using n(ℰ) = 20, n(A ∪ B)′ = 1, n(A) = 12 and n(B) = 10, write the number for each of the four regions.

  1. 1n(A ∪ B) = 20 − 1 = 19
  2. 2n(A ∩ B) = 12 + 10 − 19 = 3
  3. 3A only = 12 − 3 = 9; B only = 10 − 3 = 7
  4. 4A only: 9, A ∩ B: 3, B only: 7, outside: 1

AnswerA only: 9 A ∩ B: 3 B only: 7 Outside A ∪ B: 1

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Also searched as: 0580/22/O/N/23 · 0580_w23_qp_22 · 0580 w23 22 · question 15.
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