BASIC DEFINITIONS

1)     Set: A well-defined collection of distinct objects is called a set.

2)     Notation of Sets: Capital letters are usually used to denote or represent a set.

3)     Representation of Sets: There are two methods of representing a set. 
     (i) Roster Method 
     (ii) Set builder form.

4)     Finite and Infinite Sets: A set is finite if it contains a specific number of elements. Otherwise, a set is an infinite set.

5)     Null Set or Empty Set or Void Set: A set with no elements is an empty set .Denoted by { } or  Ø

6)     Equivalent Sets: Two finite sets A and B are said to be equivalent sets if cardinality of both sets are equal
     i.e. n (A) = n (B).

7)     Equal Sets: Two sets A and B are said to be equal if and only if they contain the same elements 
    i.e. if every element of A is in B and every element of B is in A. We denote the equality by A = B.

8)    Cardinality of a Set A: The number of elements in a finite set A, is the cardinality of A and is denoted by n(A).

9)     Universal Set: In any application of the theory of sets, the members of all sets under consideration usually belong to some fixed large set called the universal set.

10)  Subsets: If A and B are sets such that each element of A is an element of B, then we say that A is a subset of B and write A Í B.

11)  Power Set: The family of all subsets of any set S is called the power set of S. We denote the power set of S by P (S).

Set of number.

 i)  set of natural numbers , N={ 0,1,2,3,4, … }

ii) set  of positive integers, P={ 1, 2, 3, 4, … }

iii) set of all integers, Z= { …., -3, -2,-1,0,1,2,3,… }

iv) set of all real numbers, R= { …, -3, -2.5, -1/2, 0, 1, 3/2, … }