# Representation of Set

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**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

• 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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