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4024/21 May/Jun 2021, Question 5: Three-Set Venn Diagrams

Cambridge O Level Mathematics 4024 · Paper 21 (Calculator) · Calculator · 7 marks

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The question, in short

Venn diagram questions: shade a set region, then use given sets ℰ, W, X, Y to complete a diagram and answer set-notation questions.

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

Part (a) · 1 mark

Shade the region outside A but inside both B and C on the Venn diagram.

  1. 1Shade the part where circles B and C overlap that is outside circle A

AnswerRegion inside B and C but outside A shaded

Part (bi) · 3 marks

Place the ten elements of ℰ into the correct regions of the three-set Venn diagram for W, X and Y.

  1. 1W (rotational order 2): H, N, Z
  2. 2X (line symmetry): A, C, E, H, T
  3. 3Y: R, A, N, G, E
  4. 4W only: Z; W ∩ X only: H; X only: C, T; W ∩ Y only: N; X ∩ Y only: A, E; Y only: G, R; centre: none; outside: J

AnswerW only: Z W ∩ X only: H X only: C, T W ∩ Y only: N X ∩ Y only: A, E Y only: G, R W ∩ X ∩ Y: none Outside all three: J

Part (bii) · 1 mark

List the elements in X that are outside both W and Y.

  1. 1W ∪ Y = {A, E, G, H, N, R, Z}
  2. 2X ∩ (W ∪ Y)′ = {C, T}

AnswerC, T

Part (biii) · 1 mark

Find the number of elements of ℰ lying outside all three sets W, X and Y.

  1. 1Only J is outside all three circles
  2. 2n(W ∪ X ∪ Y)′ = 1

Answer1

Part (biv) · 1 mark

Complete the statement with a set expression equal to the empty set.

  1. 1No letter is in all three sets
  2. 2W ∩ X ∩ Y = ∅

AnswerW ∩ X ∩ Y

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Also searched as: 4024/21/M/J/21 · 4024_s21_qp_21 · 4024 s21 21 · question 5.
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