Lemmara logoLemmaraWorked solution

0580/13 Oct/Nov 2025, Question 23: Venn Diagrams

Cambridge IGCSE Mathematics 0580 · Paper 13 (Core) · Non-calculator · 4 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Use set notation for a shaded overlap in a Venn diagram, then complete a Venn diagram for 60 club members with 36 swimmers and find n(T′).

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

Part (a) · 1 mark

Write the set notation for the region where circles A and B overlap.

  1. 1The shaded region is in both A and B
  2. 2A ∩ B

AnswerA ∩ B

Part (bi) · 2 marks

Complete the Venn diagram using 60 people, 36 swimmers, 30 in S only and 10 outside both circles.

  1. 1S only = 30 and n(S) = 36, so T ∩ S = 36 − 30 = 6
  2. 2T only = 60 − 30 − 6 − 10 = 14
  3. 3T only: 14, T ∩ S: 6, S only: 30, outside: 10

AnswerT only: 14 T ∩ S: 6 S only: 30 Outside T and S: 10

Part (bii) · 1 mark

Find n(T′), the number of people not in set T.

  1. 1T′ = everything not in T = S only + outside
  2. 2n(T′) = 30 + 10 = 40

Answer40

Stuck on a step? Read the free lesson: Venn Diagrams

Practise more venn diagrams questions

Real 0580 past-paper questions, marked on your working like the exam, with a worked solution for every part.

Practise free on Lemmara

More past-paper questions on venn diagrams

Also searched as: 0580/13/O/N/25 · 0580_w25_qp_13 · 0580 w25 13 · question 23.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.