Representation of sets
Representation of sets
There are three methods of representing a set.
1. Statement form method
2. Roster or tabular form method
3. Rule or Set builder form method
Statement form method
In this method well defined description of the elements of the is given, and the elements are enclosed in curly brackets.
For example: 1. The set of whole numbers 29 to 35 is written as
{Whole numbers 29 to 35}
2. A set of singers of 21 years to 28 years.
Roster or Tabular form method
In roster form we list each element or member, separated by a comma, and are enclosed some curly brackets around the whole thing.
For example the set of natural numbers, form 1 to 5 is present in roster form as
{1, 2, 3, 4, 5}
set of 1 to 10 odd numbers form 1 to 10
{1, 3, 5, 7, 9}
2. In roster form we change the order of elements.
Thus the above set can also be written as
{3, 1, 7, 5, 9,}
The set of even natural numbers is written as
{2, 4, 6, 8, 10, 12…}
The dots represent that the list of even numbers continue indefinite.
3. When we write the set in roster form any element is not repeated.
For example: the set of word “book’ is
{b, o, k} or {o, b, k,}
We know that In roster form we change the order of elements.
Rule or Set builder form
In this form all the elements of a set possess a single common property.
For example in the set {a, e, i, o, u} all the elements possess a common property, each of them is a vowel in english alphabet, present the set by V we write
V = {x: x is a vowel in english alphabet}
we describe the elements of the set by using a symbol ‘x’ or any other variable followed by colon “:”after the sign of colon we write the characteristic property possessed by the elements of the set and then enclosed the whole thing with brackets.
In this description the brackets stand for “the set of all” and the colon stands for “such that”.
V = {x: x is a vowel in english alphabet}
The above example is read as the set of all x such that x is a vowel of english alphabet.