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0580/22 Oct/Nov 2022, Question 16: Venn Diagrams

Cambridge IGCSE Mathematics 0580 · Paper 22 (Extended) · Calculator · 4 marks

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The question, in short

Venn diagrams: shade the regions for G ∩ H′ and (J ∪ K′) ∩ L, then fill in the missing numbers of a three-set diagram from given totals.

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

Part (a) · 2 marks

Shade G ∩ H′ and (J ∪ K′) ∩ L.

  1. 1G ∩ H′: in G but not in H, so shade the part of G outside H
  2. 2(J ∪ K′) ∩ L: inside L and (in J or not in K)
  3. 3So shade all of L except the part of L that is in K but not in J

AnswerG ∩ H′: the part of G outside H shaded. (J ∪ K′) ∩ L: all of L shaded except the part of L that is in K but not in J

Part (b) · 2 marks

Use n(A ∩ B ∩ C) = 1, 17 outside and n(C) = 42 to finish the diagram.

  1. 1A ∩ B ∩ C (centre region) = 1
  2. 2Outside A, B and C = 17
  3. 3C only = 42 − 7 − 2 − 1 = 32

AnswerA ∩ B ∩ C: 1 C only: 32 Outside A, B and C: 17

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Also searched as: 0580/22/O/N/22 · 0580_w22_qp_22 · 0580 w22 22 · question 16.
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