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0580/23 May/Jun 2026, Question 25: Three-Set Venn Diagrams

Cambridge IGCSE Mathematics 0580 · Paper 23 (Extended) · Non-calculator · 4 marks

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The question, in short

Given integer x with ℰ = {1 to 12}, A square numbers, B from 4 to 8, C factors of 12, complete a three-set Venn diagram and find n(A ∩ B ∩ C′).

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

Part (a) · 3 marks

Place the integers 1 to 12 into the correct regions of the Venn diagram for sets A, B and C.

  1. 1A = {1, 4, 9}, B = {4, 5, 6, 7, 8}, C = {1, 2, 3, 4, 6, 12}
  2. 24 is in all three; 1 in A and C only; 6 in B and C only
  3. 39 in A only; 5, 7, 8 in B only; 2, 3, 12 in C only
  4. 410 and 11 go outside the circles

AnswerA only: 9; A ∩ B only: none; A ∩ C only: 1; A ∩ B ∩ C: 4; B ∩ C only: 6; B only: 5, 7, 8; C only: 2, 3, 12; outside: 10, 11

Part (b) · 1 mark

Find the number of integers in A ∩ B that are not in C.

  1. 1A ∩ B = {4}, but 4 is in C
  2. 2So A ∩ B ∩ C′ is empty: n = 0

Answer0

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Also searched as: 0580/23/M/J/26 · 0580_s26_qp_23 · 0580 s26 23 · question 25.
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