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4MA1/2F Jun 2019, Question 14: Set Problems

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

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The question, in short

Using the universal set 1 to 10 with A = {2, 3, 5, 7} and B = {4, 6, 8, 10}, justify a disjoint result, find missing elements, and determine set C from given conditions.

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Part (a) · 1 mark

Give a reason why sets A and B share no common members.

  1. 1A = {2, 3, 5, 7}, B = {4, 6, 8, 10}
  2. 2No number is in both sets
  3. 3So the intersection is the empty set

AnswerA and B have no members in common

Part (b) · 1 mark

State the two elements of the universal set that lie in neither A nor B.

  1. 1A ∪ B = {2, 3, 4, 5, 6, 7, 8, 10}
  2. 2Numbers in ℰ not in A ∪ B: 1 and 9

Answer1, 9

Part (c) · 2 marks

Using the stated union and intersection conditions, list every element belonging to set C.

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

Answer1, 2, 8, 9

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