Lemmara logoLemmaraWorked solution

4MA1/1H Jun 2021, Question 19: Three-Set Venn Diagrams

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 3 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Using the given three-set Venn diagram with region counts 12, 5, 9, 10, 6, 3, 4 and 8, find three specified numbers of elements.

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

Part (i) · 1 mark

Find n(A ∪ B), the number of elements in A or B.

  1. 1n(A ∪ B) counts every element that is in A or in B or in both
  2. 2These are the regions holding 12, 5, 9, 10, 6 and 3
  3. 312 + 5 + 9 + 10 + 6 + 3 = 45

Answer45

Part (ii) · 1 mark

Find n(A′ ∩ B′), the number of elements outside both A and B.

  1. 1A′ ∩ B′ is everything that is outside A and also outside B
  2. 2That is the part of C outside both A and B, holding 4, and the region outside all three sets, holding 8
  3. 34 + 8 = 12

Answer12

Part (iii) · 1 mark

Find n([A ∩ B] ∪ C), the number of elements in A ∩ B or in C.

  1. 1A ∩ B is the overlap of A and B, holding 5 + 6 = 11
  2. 2C holds 10 + 6 + 3 + 4 = 23
  3. 3The 6 in A ∩ B ∩ C lies in both of these, so count it once
  4. 411 + 23 − 6 = 28

Answer28

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

Practise more three-set venn diagrams questions

Real 4MA1 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 three-set venn diagrams

Also searched as: 4MA1 1H June 2021 · 4MA1/1H · 4ma1 jun21 1h · question 19.
Lemmara is an independent study tool, not affiliated with or endorsed by Pearson Edexcel. The worked solutions are Lemmara’s own.