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4MA1/2HR Jun 2018, Question 15: Three-Set Venn Diagrams

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2HR (Higher) · Calculator · 3 marks

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The question, in short

Using the Venn diagram with sets A, B, C in a universal set and the given element counts, find three set sizes.

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

Part (i) · 1 mark

Find the number of elements in A union B.

  1. 1n(A ∪ B) counts every element inside circle A or circle B
  2. 2Those regions hold 7, 3, 8 and 1
  3. 37 + 3 + 8 + 1 = 19

Answer19

Part (ii) · 1 mark

Find the number of elements in the complement of A intersect C.

  1. 1n(A′ ∩ C) counts the elements of C that are outside A
  2. 2These are the 1 in B ∩ C and the 4 in C only
  3. 31 + 4 = 5

Answer5

Part (iii) · 1 mark

Find the number of elements in the complement of A union the complement of B.

  1. 1All regions total 7 + 3 + 8 + 1 + 4 + 9 = 32
  2. 2A′ ∪ B′ is everything except the elements in both A and B
  3. 3A ∩ B holds 3, so 32 − 3 = 29

Answer29

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