Representation of a Set

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.

1. Descriptive 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.

2. Set Builder Form or Rule Form

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}

3. Roster Form or Tabular Form

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?

Example 1.2

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}