BASIC NUMERICAL SKILLS III Semester COMMON COURSE B Com/BBA
MODULE I
MODULE II
MODULE III
MODULE IV 7
MODULE V
The theory of sets was introduced by the German mathematician Georg Cantor in 1870. A set is well defined collection of distinct objects. The term well defined we mean that the...
The theory of sets was introduced by the German mathematician Georg Cantor in
1870. A set is well defined collection of distinct objects. The term well defined we mean that
there exists a rule with the help of which we will be able to say whether a particular object
‘belong to’ the set or does not belong to the set. The objects in a set are called its members or
elements.
The sets are usually denoted by the Capital letters of the English alphabet and the
elements are denoted by small letters.
If x is an element of a set A, we write X∈A (read as x belong to A). If x is not an element
of A then we write XøA (read as x does not belong to A).
Representation of a Set or Methods of describing a Set
A set is often representation in two ways:
(1) Roster method or tabular or enumeration method.
(2) Set builder method or Rule or Selector method.
Tabular Method
In this method, a set is described by listing the elements, separated by commas and are
enclosed within braces. For example the set of first three odd numbers 1,3,5 is represented as :
A = {1, 3, 5}
Set Builder Method
In this method, the set is represented by specifying the characteristic property of its
elements. For example the set of natural numbers between 1 and 25 is represented as:
A = {x: x ∈ N and 1 < x < 25 }
TYPES OF SETS
1. Null Set or Empty Set or Void Set
A set containing no element is called a null set. It is denoted by { } or Ø
Eg:‐ the set of natural numbers between 4 and 5.
2. Singleton or Unit Set
A Set containing a single element is called singleton set
Eg:‐ Set of all positive integers less than 2
3. Finite Set
A Set is said to be a finite set if it consist only a finite number of elements. The null set
is regarded as a finite set.
Eg:‐ the set of natural numbers less than 10
Basic Numerical Skills 4
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