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In descriptive form, a set is described in words.

**Representation of a Set**

The collection of odd numbers can be described in
many ways:

1) “The set
of odd numbers” is a fine description, we understand it well.

2) It can be
written as {1, 3, 5, …} and you know what I mean.

3) Also, it
can be said as the collection of all numbers *x* where *x* is an odd
number.

All of them are equivalent and useful. For
instance,the two descriptions “The collection of all solutions to the equation *x–*5 = 3” and {8} refer to the same set.

A set can be represented in any one of the
following three ways or forms:

1)
Descriptive Form.

2)
Set-Builder Form or Rule Form.

3) Roster
Form or Tabular Form.

In descriptive form, a set is described in words.

For example,

(i) The set of all vowels in English alphabets.

(ii)The set of whole numbers.

In set builder form, all the elements are described
by a rule.

For example,

(i) *A *= {*x *:*
x *is a vowel in English alphabets}

(ii) *B *=
{*x*|*x *is a whole number}

A set can be described by listing all the elements
of the set.

For example,

(i) *A *= {*a*,*
e*,* i*,* o*,* u*}

(ii) *B *=
{0,1,2,3,…}

Can this form of representation be possible always?

Write the set of letters of the
following words in Roster form

(i) ASSESSMENT (ii) PRINCIPAL

*Solution*

(i) ASSESSMENT

*A*= {*A*,*
S*,* E*,* M*,* N*,* T*}

(ii) PRINCIPAL

*B*={*P*,*
R*,* I*,* N*,* C*,* A*,*
L*}

Tags : Mathematics , 9th EM Mathematics : Set Language

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9th EM Mathematics : Set Language : Representation of a Set | Mathematics

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