# Representation of Set

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In representation of set there are three ways :

Representation of set

1) A set is denoted by a capital letter.
Example : set A, set B, set N etc.

2) The elements of a set are denoted by small letters.All elements are written in { } (curly) brackets separated by , (comma).
Example : a,b,c,x ,y etc.

3) In set notation, elements are not repeated.
Example : A is a set of letters in the word good,
then set A = { g,o,d}.

4) The order of elements in a set does not matter.

Notations :

1) Roster Notation ( Tabular form)

In this form, we enumerate or list all the element.

Examples :

1) A is a set of whole numbers less than 6.

A = { 0,1,2,3,4,5}

2) C is the set of letters in the word excellent.

C = { e, x, c, l, n, t }

Set-builder form ( Rule method)

In this method , we specify the rule or property or statement.
A = { x | x has a property of p}
This is read as A is the set of elements x such that( | ) x has a property p.

Examples :

1) Given : A = { 2,4,6,8,10,12}

Solution :
In set A all the elements are even natural number up to 12.So this is the rule for the set A

So set builder notation will be

A = { x | x is an even natural number, x ≤ 12}

2) B = { 4,5,6,7}

Solution :
In set B all the elements are natural numbers between 3 and 8.This is the rule.

So set builder notation will be

B ={ x | x is a natural number, 3 < x < 8}

Or
B = { x | x ∈N, 3 < x < 8}.
Set Theory

Sets
Representation of Set
Cardinal Number
Types of Sets
Pairs of Sets
Subset
Complement of Set
Union of the Sets
Intersection of Sets
Operations on Sets
De Morgan's Law
Venn Diagrams
Venn-diagrams for sets
Venn-diagrams for different situations
Problems on Intersection of Two Sets
Problems on Intersection of Three Sets