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4024/11 May/Jun 2020, Question 15: Venn Diagrams

Cambridge O Level Mathematics 4024 · Paper 11 (Non-calculator) · Non-calculator · 4 marks

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The question, in short

Given ℰ = integers 1 to 10, F = factors of 24, S = square numbers, complete a Venn diagram and find n(F ∪ S)′; then shade P ∩ Q ∩ R′ on a three-set diagram.

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

Part (ai) · 2 marks

Place each integer from 1 to 10 into the correct region of the two-circle Venn diagram for factors of 24 and square numbers.

  1. 1F = {1, 2, 3, 4, 6, 8}, S = {1, 4, 9}
  2. 2F ∩ S: 1, 4
  3. 3F only: 2, 3, 6, 8; S only: 9
  4. 4Outside F and S: 5, 7, 10

AnswerF only: 2, 3, 6, 8 F ∩ S: 1, 4 S only: 9 Outside F and S: 5, 7, 10

Part (aii) · 1 mark

Find the number of elements in the complement of F ∪ S.

  1. 1(F ∪ S)′ = {5, 7, 10}
  2. 2n(F ∪ S)′ = 3

Answer3

Part (b) · 1 mark

On the three-circle Venn diagram, shade the region for P ∩ Q ∩ R′.

  1. 1Shade the region that is inside both P and Q but outside R

AnswerRegion inside P and Q but outside R shaded

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Also searched as: 4024/11/M/J/20 · 4024_s20_qp_11 · 4024 s20 11 · question 15.
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