SETS
It has been said that, A set is a collection of, well-defined distinct objects. The object of a set are called members or elements of the set. We call a set a “well-defined collection of objects” because we can decide ( with absolute certainty ) whether a given project is a member of the set.
Types of Set –
a) The set of all integers
b) The set of vowels of the English alphabet
c) The set of rivers/cities/fruits/district of any countries or world
d) The set of students of class six of your school/college.
we usually denote a set by a capital letter of the English alphabet, such as A, B, C, X, Y, Z and its elements are written by small letters of English alphabet, such as a, b, c, x, y, & z.
If A is an element of set X, we write a ∈ X and we have to read as ‘a’ belongs to the set ‘X’. but If a is not an element of the sets ‘X’, then we should write as a ∉ X and should read as ‘a' is not belongs to set X ’
There are some special form of Sets are given below -
1) Rule Method or Set Builder Form
2) Roster Method or Tabular Form
3) Finite Set
4) Infinite Set
5) Empty Set
6) Universal Set
7) Singleton Set
8) Equivalent Set
9) SubSet
10) Super Set
Some Special Sets –
1) N = { 1, 2, 3, 4, ……… } (Set of Natural Numbers)
2) W = { 0, 1, 2, 3,………. } (Set of whole numbers)
3) Z = {………, -3, -2, -1, 0, 1, 2, 3,………} (Set of Integers), This is also denoted as ‘I’