Representation of Set

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}.

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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

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