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4024/23 May/Jun 2026, Question 11: Venn Diagrams

Cambridge O Level Mathematics 4024 · Paper 23 (Calculator) · Calculator · 4 marks

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The question, in short

Given ℰ = {1,...,10}, A = factors of 10 and B = multiples of 2, place elements in a Venn diagram and work with set combinations.

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

Part (a) · 2 marks

Place each element of ℰ into the correct region of the two-circle Venn diagram for sets A and B.

  1. 1A = {1, 2, 5, 10}, B = {2, 4, 6, 8, 10}
  2. 2Overlap A ∩ B: 2, 10
  3. 3A only: 1, 5; B only: 4, 6, 8
  4. 4Outside both: 3, 7, 9

AnswerA only: 1, 5; A ∩ B: 2, 10; B only: 4, 6, 8; outside both circles: 3, 7, 9

Part (b) · 1 mark

List the elements that lie outside both A and B, i.e. (A ∪ B)′.

  1. 1A ∪ B = {1, 2, 4, 5, 6, 8, 10}
  2. 2(A ∪ B)′ = {3, 7, 9}

Answer3, 7, 9

Part (c) · 1 mark

Find the number of elements in A′ ∪ B.

  1. 1A′ ∪ B is everything except A only {1, 5}
  2. 2n(A′ ∪ B) = 10 − 2 = 8

Answer8

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Also searched as: 4024/23/M/J/26 · 4024_s26_qp_23 · 4024 s26 23 · question 11.
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