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4MA1/2H Jun 2019, Question 3: Set Problems

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

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The question, in short

Using sets ℰ, A and B given, justify why A and B share no elements, find x outside their union, and determine set C from the stated conditions.

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

Part (a) · 1 mark

Explain why sets A and B have no common members.

  1. 1A contains the numbers 2, 3, 5, 7
  2. 2B contains the numbers 4, 6, 8, 10
  3. 3No number appears in both A and B
  4. 4Therefore, A ∩ B = ∅

AnswerThere are no members that are in both A and B

Part (b) · 1 mark

Given x is in ℰ but not in A ∪ B, state the two possible values of x.

  1. 1E = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
  2. 2A ∪ B = {2, 3, 4, 5, 6, 7, 8, 10}
  3. 3x ∈ E and x ∉ A ∪ B
  4. 4Numbers in E but not in A ∪ B are 1 and 9
  5. 5So x = 1 or x = 9

Answer1 and 9

Part (c) · 2 marks

Using the given conditions on C, list all members of set C.

  1. 1A ∪ B ∪ C = ℰ, so 1 and 9 must be in C
  2. 2A ∩ C = {2}: 2 is in C, but 3, 5, 7 are not
  3. 3B ∩ C′ = {4, 6, 10}: 4, 6, 10 are not in C, but 8 is
  4. 4So C contains 1, 2, 8, 9

Answer1, 2, 8, 9

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