A well defined collection of objects is called a set. A given collection of objects is said to be well defined, if we can definitely say whether a given particular object belongs to a collection or not. The objects in a set are called its members or elements. The sets are denoted by capital letters A, B, C, P, Q, R, etc.
Representation of a Set
The set are generally represented in the following two ways:
• Roster Form or Tabular Form
In the roster form, we list all the members of the set within {} and separate them by commas.
Example: A = set of all factors of 24
All factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.
Therefore, A = {1, 2, 3, 4, 6, 8, 12, 24}
• Set-Builder Form
In the set-builder form, we list the property or properties satisfied by all the elements of the set. It is written as {x: x satisfies properties P}, which is read as ‘the set of those entire x such that each x has properties P’.
Example: Write set A = {1, 2, 3, 4, 5, 6, 7} in the set builder form.
Clearly, A = set of all natural numbers less than 8.
Thus, in the set-builder form, we write it as
A = {x: x N and x < 8}
