Representation of Sets:
There are two ways to represent a given set.
1. Roster or Tabular Form or list form: In this form, list all the members of the set, separate these by commas and enclose these within braces (curly brackets)
For Example:
i) The set S of even natural numbers less than 12 in the tabular form is written as S = { 2, 4, 6, 8, 10 }. Note that 8 \(\in\) S while 7 \(\notin\) S.
2. Set Builder or rule form: In this form, write one or more ( if necessary) variables ( say x, y etc.) representing an arbitrary member of the set, this is followed by a statement or a property which must be satisfied by each member of the set.
For Example:
i) The set S of even natural numbers less than 12 in the set builder form is written as S= { x/x is an even natural number less than 12}
Representation of Sets:
There are two ways to represent a given set.
1. Roster or Tabular Form or list form: In this form, list all the members of the set, separate these by commas and enclose these within braces (curly brackets)
For Example:
i) The set S of even natural numbers less than 12 in the tabular form is written as S = { 2, 4, 6, 8, 10 }. Note that 8 \(\in\) S while 7 \(\notin\) S.
2. Set Builder or rule form: In this form, write one or more ( if necessary) variables ( say x, y etc.) representing an arbitrary member of the set, this is followed by a statement or a property which must be satisfied by each member of the set.
For Example:
i) The set S of even natural numbers less than 12 in the set builder form is written as S= { x/x is an even natural number less than 12}
Some standard Sets:
We enlist below some sets of numbers which are most communal used in the study of sets:
i) The set of natural numbers ( or positive integers). It is usually denoted by N.
i.e. N= { 1, 2, 3, 4, ......}
ii) The set of whole numbers. It is usually denoted by W. I.e. W = { 0, 1, 2, 3, ....}.
iii) The set of integers. It is usually denoted by Z. i. E. Z = { ..... -3, -2, -1, 0, 1, 2, 3, .....}
iv) The set of rational numbers, It is usually denoted by Q i.e., Q = { x : x is a ration number } or { x : x \(\frac {m}
{n}\), where m and n are integers and n \(\ne\) 0}
v) The set of real numbers. It is usually denoted by R. i.e. R = { x : x is a real number} or R = { x is either a rational number or an irrational number}
Note:- i = \(\sqrt{-1}\)