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4024/11 Oct/Nov 2020, Question 14: Venn Diagrams

Cambridge O Level Mathematics 4024 · Paper 11 (Non-calculator) · Non-calculator · 3 marks

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The question, in short

Venn diagram shading task plus two set-counting problems about 42 people, 30 Spanish speakers and 20 French speakers, asking for extreme overlap and neither counts.

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

Part (a) · 1 mark

Shade the region on the Venn diagram representing the set (P ∪ Q) ∩ R′.

  1. 1(P ∪ Q): everything in P or Q
  2. 2∩ R′: remove any part inside R
  3. 3Shade all of P and Q except the parts inside R

AnswerShade all of P and Q except the parts inside R

Part (bi) · 1 mark

With 42 people, 30 speaking Spanish and 20 French, find the minimum number speaking both.

  1. 1Smallest overlap when everyone speaks at least one language
  2. 2Both = 30 + 20 − 42 = 8

Answer8

Part (bii) · 1 mark

Using the same 42 people, 30 Spanish and 20 French, find the maximum number speaking neither language.

  1. 1Largest 'neither' when all French speakers also speak Spanish
  2. 2Neither = 42 − 30 = 12

Answer12

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Also searched as: 4024/11/O/N/20 · 4024_w20_qp_11 · 4024 w20 11 · question 14.
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