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Sets and Venn Diagrams
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Sets and Venn Diagrams

lesson introduction

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?

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A venn diagram uses circles to represent sets

The diagram creates a region in the middle for values which overlap between two sets.

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

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

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We can assign values to each set from the universal

xx can be 1,2,3,4,...,191, 2, 3, 4, ..., 19. Members of A (even numbers) can be 2,4,6,8,10,12,14,16,182, 4, 6, 8, 10, 12, 14, 16, 18. Members of B (square numbers) can be 4,9,164, 9, 16.

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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.

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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}

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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}

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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}A' = \{1, 3, 5, 7, 9, 11, 13, 15, 17, 19\}. Similarly, values not in set B can be notated as B'.

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