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0580/22 May/Jun 2021, Question 12: Set Notation

Cambridge IGCSE Mathematics 0580 · Paper 22 (Extended) · Calculator · 3 marks

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The question, in short

Sets question using ℰ = integers greater than 2, with A primes, B odds, C squares: describe a set, label a Venn diagram, and shade a region.

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

Part (ai) · 1 mark

Describe the numbers that belong to both the complement of B and set C.

  1. 1B′ = numbers that are not odd, i.e. even numbers
  2. 2B′ ∩ C = even numbers that are also square numbers
  3. 3Even square numbers

AnswerEven square numbers

Part (aii) · 1 mark

Fill in the missing set labels on the given Venn diagram.

  1. 1All primes greater than 2 are odd, so A lies completely inside B.
  2. 2Some square numbers are odd (9, 25) and some are not (4, 16), so C overlaps B.
  3. 3Large left circle: B; small circle inside it: A; right circle: C

AnswerLarge left circle: B; small circle inside it: A; right circle: C

Part (b) · 1 mark

Shade the region representing D′ ∪ (E ∩ F)′ on the three-circle Venn diagram.

  1. 1D′ ∪ (E ∩ F)′ = (D ∩ E ∩ F)′
  2. 2It is everything except the region in all three circles.
  3. 3Shade everything inside ℰ except the region D ∩ E ∩ F

AnswerEverything inside ℰ shaded except the region D ∩ E ∩ F

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Also searched as: 0580/22/M/J/21 · 0580_s21_qp_22 · 0580 s21 22 · question 12.
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