4MA1/1FR Jun 2020, Question 12: Venn Diagrams
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1FR (Foundation) · Calculator · 3 marks
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The question, in short
Given ℰ = whole numbers 1 to 15, A = even numbers and B = {3, 6, 9, 12, 15}, place all elements in the correct regions of the Venn diagram.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 3 marks
- 1E = {1, 2, 3, ..., 15}
- 2A = {even numbers} = {2, 4, 6, 8, 10, 12, 14}
- 3B = {3, 6, 9, 12, 15}
- 4Numbers in both A and B: 6 and 12, so write 6 and 12 in the overlap
- 5Numbers in A but not B: 2, 4, 8, 10, 14, so write these in A only
- 6Numbers in B but not A: 3, 9, 15, so write these in B only
- 7The numbers left over are 1, 5, 7, 11, 13, so write these outside both circles
- 8Venn diagram complete: A only 2, 4, 8, 10, 14; overlap 6, 12; B only 3, 9, 15; outside 1, 5, 7, 11, 13
AnswerA only: 2, 4, 8, 10, 14; A ∩ B: 6, 12; B only: 3, 9, 15; outside both circles: 1, 5, 7, 11, 13
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