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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.

Let universal = $\{x : 0 < x < 20\}$

**A = {even numbers}** and **B = {square numbers}**

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 $4, 9, 16$.

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**.

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}

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}

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'.