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4MA1/2HR Jun 2022, Question 4: Set Notation

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2HR (Higher) · Calculator · 5 marks

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The question, in short

Using the universal set from 9 to 20, with A as multiples of 3 and B as odd numbers, find set intersections, unions, membership and a possible set C.

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

Part (ai) · 1 mark

Give the elements shared by A and B.

  1. 1Identify multiples of 3 in E: 9, 12, 15, 18
  2. 2Identify odd numbers in E: 9, 11, 13, 15, 17, 19
  3. 3Find common elements in both A and B: 9, 15

Answer9, 15

Part (aii) · 1 mark

Give all elements belonging to A or B or both.

  1. 1List all multiples of 3: 9, 12, 15, 18
  2. 2List all odd numbers: 9, 11, 13, 15, 17, 19
  3. 3Combine all unique elements from both sets: 9, 11, 12, 13, 15, 17, 18, 19

Answer9, 11, 12, 13, 15, 17, 18, 19

Part (b) · 1 mark

Decide whether 24 belongs to A, tick Yes or No, and justify your choice.

  1. 1Check if 24 is in the universal set E
  2. 2E contains numbers from 9 to 20
  3. 324 is not between 9 and 20
  4. 4So 24 is not in A

AnswerNo, because the universal set only runs from 9 to 20, so 24 is not in A

Part (c) · 2 marks

Give one set C with 4 elements whose members not in B are 10 and 18.

  1. 1B' is the complement of B, so even numbers in E: 10, 12, 14, 16, 18, 20
  2. 2C ∩ B' = {10, 18}, so C must include 10 and 18
  3. 3The other two members of C must not be in B', so they must be odd
  4. 4Choose any two odd numbers from E: e.g. 9, 11
  5. 5So one possible set C is 10, 18, 9, 11

Answer10, 18 and two from 9, 11, 13, 15, 17, 19

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