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4MA1/1H Jun 2024, Question 7: Set Notation

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 5 marks

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The question, in short

Using ℰ = {23,...,34}, A = evens, B = {23,29,31}, C = multiples of 3, find set combinations, test whether B ∩ C is empty, and list a 4-member set D disjoint from A ∪ C.

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Part (ai) · 1 mark

List the members of B ∪ C.

  1. 1B = {23, 29, 31}
  2. 2C = multiples of 3 in ℰ: 24, 27, 30, 33
  3. 3B ∪ C includes all elements in B or C: 23, 24, 27, 29, 30, 31, 33

Answer23, 24, 27, 29, 30, 31, 33

Part (aii) · 1 mark

List the members of A′ ∩ C.

  1. 1A = even numbers in ℰ: 24, 26, 28, 30, 32, 34
  2. 2A′ = not in A: 23, 25, 27, 29, 31, 33
  3. 3C = multiples of 3: 24, 27, 30, 33
  4. 4A′ ∩ C = elements in both A′ and C: 27, 33

Answer27, 33

Part (b) · 1 mark

Decide whether B ∩ C = ∅, tick Yes or No, and give a reason.

  1. 1B = {23, 29, 31}
  2. 2C = {24, 27, 30, 33}
  3. 3No number is in both B and C
  4. 4B ∩ C has no members
  5. 5So B ∩ C = ∅
  6. 6Yes, there are no multiples of 3 in set B

AnswerYes, because B = {23, 29, 31} contains no multiples of 3, so B and C have no members in common

Part (c) · 2 marks

List the 4 members of set D, given D ∩ (A ∪ C) = ∅.

  1. 1A ∪ C = all even numbers and all multiples of 3 in ℰ
  2. 2A ∪ C = {24, 26, 27, 28, 30, 32, 33, 34}
  3. 3D ∩ (A ∪ C) = ∅ means D shares no members with A ∪ C
  4. 4So D must be made from numbers not in A ∪ C
  5. 5Numbers not in A ∪ C: 23, 25, 29, 31
  6. 6These are all odd and not multiples of 3
  7. 7D has 4 members: 23, 25, 29, 31

Answer23, 25, 29, 31

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