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4MA1/2FR Jun 2024, Question 20: Set Notation

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

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The question, in short

Using ℰ = {1,...,10}, A = factors of 6 and B = primes, find set combinations, explain why A ∩ B is not empty, and find a 4-member set C meeting given intersection conditions.

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Part (ai) · 1 mark

List the members of A ∪ B.

  1. 1Factors of 6 are 1, 2, 3, 6 so A = {1, 2, 3, 6}
  2. 2Prime numbers in E are 2, 3, 5, 7 so B = {2, 3, 5, 7}
  3. 3A ∪ B = {1, 2, 3, 5, 6, 7}

Answer1, 2, 3, 5, 6, 7

Part (aii) · 1 mark

List the members of A′.

  1. 1A = {1, 2, 3, 6}
  2. 2E = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
  3. 3A′ is all elements in E not in A
  4. 4So A′ = {4, 5, 7, 8, 9, 10}

Answer4, 5, 7, 8, 9, 10

Part (b) · 1 mark

Explain why Harpreet's claim that A ∩ B = ∅ is incorrect.

  1. 1A = {1, 2, 3, 6}
  2. 2B = {2, 3, 5, 7}
  3. 32 is a factor of 6 and is prime
  4. 43 is a factor of 6 and is prime
  5. 5So A ∩ B = {2, 3}
  6. 6Therefore A and B are not disjoint

Answer2 and 3 are in both sets A and B

Part (c) · 2 marks

List the 4 members of set C satisfying the stated intersection conditions.

  1. 1A = {1, 2, 3, 6} and B = {2, 3, 5, 7}
  2. 22 and 3 are in both A and B, so C cannot contain them
  3. 3So C takes 1 and 6 from A only, and 5 and 7 from B only
  4. 4C = {1, 5, 6, 7}

Answer1, 5, 6, 7

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Also searched as: 4MA1 2FR June 2024 · 4MA1/2FR · 4ma1 jun24 2fr · question 20.
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