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0580/41 May/Jun 2023, Question 9: Three-Set Venn Diagrams

Cambridge IGCSE Mathematics 0580 · Paper 41 (Extended) · Calculator · 8 marks

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The question, in short

Use a Venn diagram with sets X and Y to list elements, find a count, shade regions, and complete and evaluate a three-set problem with ℰ = positive integers < 13.

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

Part (ai) · 1 mark

List the elements that belong to set X from the Venn diagram.

  1. 1X contains the letters in the X circle, including the overlap
  2. 2X = {r, l, t, e, a}

Answerr, l, t, e, a

Part (aii) · 1 mark

Find n(Y′), the number of elements not in set Y.

  1. 1Y′ is everything outside Y
  2. 2Only r and l are outside Y
  3. 3n(Y′) = 2

Answer2

Part (b) · 2 marks

Shade the region for P ∪ Q and the region for P′ ∩ Q in the two Venn diagrams.

  1. 1P ∪ Q: shade everything inside P or Q, including the overlap
  2. 2P′ ∩ Q: shade the part of Q that is not in P (the crescent of Q only)

AnswerP ∪ Q: both circles shaded; P′ ∩ Q: Q only (the part of Q outside P) shaded

Part (ci) · 3 marks

Complete the Venn diagram for A, B and C using ℰ = positive integers < 13, A = x < 9, B = even, C = multiple of 3.

  1. 1ℰ = {1, 2, …, 12}, A = {1, …, 8}, B = {2, 4, 6, 8, 10, 12}, C = {3, 6, 9, 12}
  2. 2In all three: 6; A and B only: 2, 4, 8; A and C only: 3; B and C only: 12
  3. 3A only: 1, 5, 7; B only: 10; C only: 9
  4. 4Outside all circles: 11

AnswerA only: 1, 5, 7; A ∩ B only: 2, 4, 8; A ∩ C only: 3; A ∩ B ∩ C: 6; B only: 10; B ∩ C only: 12; C only: 9; outside: 11

Part (cii) · 1 mark

Find n(A′ ∪ (B ∩ C)).

  1. 1A′ = {9, 10, 11, 12}
  2. 2B ∩ C = {6, 12}
  3. 3A′ ∪ (B ∩ C) = {6, 9, 10, 11, 12}
  4. 4n = 5

Answer5

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Also searched as: 0580/41/M/J/23 · 0580_s23_qp_41 · 0580 s23 41 · question 9.
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