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Sets can be expressed in three ways:
  1. The set of all even natural numbers.
  2. Set \(A =\) {\(x  |  x\) is an even natural number}.
  3. Set \(A =\)  2,4,6,8,10,....
All the above lines represent the same meaning in different forms.
Thus, a set can be represented in any one of the following ways.
  1. Descriptive form.
  2. Set builder form/Ruler form.
  3. Roster form/Tabular form.
A set is described in words is called descriptive form.
  1. The set of odd natural numbers less than \(20\).
  2. The set of all first four months of the year.
A rule describes all the elements is called a set builder or ruler form.
  1. A=x:xisanoddnaturalandx<20
  2. B=x|xisthefirstfourmonthsoftheyear
A set is described by listing all the elements of it that are called as a Roster form.
  1. A=1,3,5,7,9,11,13,15,17,19
  2. B=January,February,March,April