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4MA1/1HR Jan 2022, Question 17: Set Notation

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

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The question, in short

Using the Venn diagram with region counts 6, 3, 8, 2, 5 and 4, find four set sizes involving A, B and C.

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. 1A holds 6 and 3; B holds 3, 8 and 2
  2. 2A ∪ B counts each region once: 6 + 3 + 8 + 2 = 19

Answer19

Part (ii) · 1 mark

Find the number of elements in A intersect C.

  1. 1On the diagram A and C do not overlap at all
  2. 2So n(A ∩ C) = 0

Answer0

Part (iii) · 1 mark

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

  1. 1B ∩ C′ is the part of B that is outside C
  2. 2That is the 3 and the 8, so 3 + 8 = 11

Answer11

Part (iv) · 1 mark

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

  1. 1A′ ∪ B′ ∪ C′ leaves out only what is in all three sets at once
  2. 2Nothing is in all three, so nothing is left out
  3. 3Total = 6 + 3 + 8 + 2 + 5 + 4 = 28

Answer28

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