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Sets and Venn Diagrams
Sets and Venn Diagrams
Venn diagrams are a tool for visualising crossover between two groups.
Set notation allows us to easily list members of a collection of numbers or objects, but we can also represent sets visually using venn diagrams.
100 is a member of set M.
M = {positive multiples of 10 under 1000}
How would you notate this?
A venn diagram uses circles to represent sets
The diagram creates a region in the middle for values which overlap between two sets.
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/jET927gURhdbcGvVBQ0A.png)
Let universal = {x:0<x<20}
A = {even numbers} and B = {square numbers}
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/jET927gURhdbcGvVBQ0A.png)
We can assign values to each set from the universal
x can be 1,2,3,4,...,19. Members of A (even numbers) can be 2,4,6,8,10,12,14,16,18. Members of B (square numbers) can be 4,9,16.
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/jET927gURhdbcGvVBQ0A.png)
Each circle represents a set
We can place values in locations on the diagram depending on their relation to the sets. Numbers that do not belong to either set are placed on the outside.
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/Ui3WBBkoRlaB8RUG9yHF.png)
Numbers in the middle fit both sets
This is the intersection and can be written as A ∩ B. In this example, A ∩ B = {4,16}
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/Ui3WBBkoRlaB8RUG9yHF.png)
Elements in either set are called the union
These can be written as A ∪ B. In this example, A ∪ B = {2, 4, 6, 8, 9, 10, 12, 14, 16, 18}
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/Ui3WBBkoRlaB8RUG9yHF.png)
Elements that are not in set A can be notated as A'
In this case A′={1,3,5,7,9,11,13,15,17,19}. Similarly, values not in set B can be notated as B'.
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/Ui3WBBkoRlaB8RUG9yHF.png)