PURE MATHEMATICS - Algebra

 

Number Set Theory

 

 

Introduction

Common Sets

Venn Diagrams

Sub-Sets

 

 

 

Introduction

 

A set is a collection of objects, numbers or characters.

 

{abcdef....wxyz}  {1,2,3,4,...45, 46, 47}   etc.

 

Note how the set is enclosed in brackets {.....}

 

 

A definite set is one in which all its members are known.

 

Sets are given uppercase letters: A, B, C, etc.

 

The elements of sets are given lowercase letters: a, b, c,..etc.

 

An element x belonging to the set A is written:

 

x is an element of the set A

 

A constraint bar {...|...} is for setting a property that all members satisfy.

 

e.g. A{x l x has the colour blue} - all elements of A are blue

 

 

back to top

 

 

Common Sets

 

set types

 

 

back to top

 

 

Venn Diagrams

 

Venn Diagrams are used to visualise sets and their relations to one another.

 

 

venn diagram#1

 

 

Above is a diagramatic representation of set A.

 

The set can be represented mathematically as: A{1,3,5,7,9} .

 

Note that set A(the circle) is a subset of the Universal set(the rectangle).

 

 

 

venn diagram complement

 

 

A' (A-dash)is called the complement of A.

 

It contains all elements that are not members of A.

 

A and A' together make up the Universal set.

 

 

union

 

 

The union of sets A and B contains all of the elements from both sets.

 

union of sets

 

 

intersection

 

 

The intersection of sets A and B contains a particular group of elements that exist in set A and in set B.

intersection

 

 

back to top

 

 

Subsets

 

If B is a subset of A. Then all of the elements of B are also in A.

 

 

venn diagram B is a subset of A

 

 

B is a subset of A

 

 

 

 

 

back to top

 

 

 

this week's promoted video

 

 from Physics Trek

 

 

creative commons license

All downloads are covered by a Creative Commons License.
These are free to download and to share with others provided credit is shown.
Files cannot be altered in any way.
Under no circumstances is content to be used for commercial gain.

 

 

 

 

©copyright a-levelmathstutor.com 2020 - All Rights Reserved