4MA1/2F Jan 2023, Question 18: Venn Diagrams
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2F (Foundation) · Calculator · 3 marks
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The question, in short
Using ℰ = {11 to 20}, A = even numbers, A ∩ B = {12, 16, 20} and (A ∪ B)′ = {17, 19}, complete the Venn diagram showing sets ℰ, A and B.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 3 marks
- 1A = even numbers in ℰ = {12, 14, 16, 18, 20}
- 2A ∩ B = {12, 16, 20}, so A only = {14, 18}
- 3(A ∪ B)′ = {17, 19} goes outside both circles
- 4The numbers left, 11, 13 and 15, go in B only
- 5A only: {14, 18}, A ∩ B: {12, 16, 20}, B only: {11, 13, 15}, outside: {17, 19}
AnswerVenn diagram with regions filled as follows: A only: {14, 18}, B only: {11, 13, 15}, A ∩ B: {12, 16, 20}, (A ∪ B)ʹ: {17, 19}
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