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The elements 1 and 2 have been entered on this Venn diagram - OCR - GCSE Maths - Question 9 - 2021 - Paper 3

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Question 9

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The elements 1 and 2 have been entered on this Venn diagram. Complete the Venn diagram to show all of the elements.

Worked Solution & Example Answer:The elements 1 and 2 have been entered on this Venn diagram - OCR - GCSE Maths - Question 9 - 2021 - Paper 3

Step 1

Identify the elements in Set A and Set B

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Answer

Set A consists of odd numbers from the universal set, which are {1, 3, 5, 7, 9, 11, 13, 15}. Set B consists of multiples of 5 from the universal set, which are {5, 10, 15}.

Step 2

Determine the elements in the intersection of Set A and Set B

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Answer

The intersection of Set A and Set B includes elements that are both odd and multiples of 5. Thus, the intersection is {15}.

Step 3

List the elements only in Set A

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Answer

The elements in Set A that are not in Set B are {1, 3, 5, 7, 9, 11, 13}.

Step 4

List the elements only in Set B

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Answer

The elements in Set B that are not in Set A are {5, 10}.

Step 5

Complete the Venn Diagram

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Answer

In the Venn diagram:

  • Circle A will contain {1, 3, 7, 9, 11, 13, 15}.
  • Circle B will contain {5, 10, 15}.
  • The intersection will be {15}, showing the common element.

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