Representation of Sets

Representation of Sets

A set is often described in the following two forms:
(i) Roster form
In this form a set is described by listing elements, separated by commas, within braces {}.
Illustration: If A is set of all prime numbers less than 11 then A= {2, 3, 5, 7} represents the roster form.
Example  Write the following sets in the roaster form.
 A = {x | x is a positive integer less than 10 and 2x– 1 is an odd number}

2x – 1 is always an odd number for all positive integral values of x. In particular,
2x – 1 is an odd number for x = 1, 2, ... , 9. Thus, A = {1, 2, 3, 4, 5, 6, 7, 8, 9}.

 (ii) Set-Builder form
In this form a set is described by a characterizing property C(x) of its elements x. In such a case the set is described by  {x: C(x) holds} or {x| C(x) holds}, which is read as ‘the set of all x such that C(x) holds’. The symbol | or : is read as “such that”.

The general form is, A = { x : property }

So, the set builder form is A = {x: x=2n, n ∈ N and 1  ≤ n ≤ 4}

Example: The set of reciprocals of all natural numbers is represents as:
{x: x is reciprocal of a natural number} or {x: x=1/n , n ∈  N}