Representation of Sets

Sets can be represented in two ways:

1. Roster Form or Tabular form
2. Set Builder Form

Roster Form

In roster form, all the elements of the set are listed, separated by commas and enclosed between curly braces { }. 

Example: If set represents all the leap years between the year 1995 and 2015, then it would be described using Roster form as:

A ={1996,2000,2004,2008,2012}

Now, the elements inside the braces are written in ascending order. This could be descending order or any random order. As discussed before, the order doesn’t matter for a set represented in the Roster Form. 

Also, multiplicity is ignored while representing the sets. E.g. If L represents a set that contains all the letters in the word ADDRESS, the proper Roster form representation would be

L ={A,D,R,E,S }= {S,E,D,A,R}  

L≠ {A,D,D,R,E,S,S}

Set Builder Form

In set builder form, all the elements have a common property. This property is not applicable to the objects that do not belong to the set. 

Example: If set S has all the elements which are even prime numbers, it is represented as:

S={ x: x is an even prime number}

where ‘x’ is a symbolic representation that is used to describe the element.

‘:’ means ‘such that’

‘{}’ means ‘the set of all’

So, S = { x:x is an even prime number } is read as ‘the set of all x such that x is an even prime number’. The roster form for this set S would be S = 2. This set contains only one element. Such sets are called singleton/unit sets.

Another Example:

F = {p: p is a set of two-digit perfect square numbers}

How?

F = {16, 25, 36, 49, 64, 81}

We can see, in the above example, 16 is a square of 4, 25 is square of 5, 36 is square of 6, 49 is square of 7, 64 is square of 8 and 81 is a square of 9}. 

Even though, 4, 9, 121, etc., are also perfect squares, but they are not elements of the set F, because the it is limited to only two-digit perfect square.