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SET
THEORY

2. SET THEORY CONTENTS
• 1. Meaning and definition.
2. Representation of a set.
3. Set notation.
4. Types and kinds of set.
5. Sub-set and Universal set.
6.Union OF SET
7. Intersection of set.
8. DE-MORGAN’S LAW.

3. MEANING AND DEFINITATION
• The concept of set was introduce in the end of
19th century by German mathematician
GEORGE CANTER (1845-1918)
• A set a structure ,representing an unordered
collection (group , plurality) of zero or more
distinct(different) objects.
• The objects that makes up a set is called
member or objects of the set.
• Set theory deals with operations between
,relations among ,and statements about sets.

4. REORESENTATION OF SET
A set can be represented by two method
(1). Tabular or Roster method = Under this method
,the element of a set are enumerated or listed
within parentheses ( ), , , separated by
commas (,) .
(2). Builder method = Under this method , the
element are indicated by description of their
characteristics or properties .( x: x is a element of
a set )

5. SET NOTATION
• Normally set are denoted by capital letters of
English alphabet like A,B,C,D,…..X,M ,Z
.Example A=( 1,2,3,4,5,6).
• If X is an element of a set A ,it is written as X is
not equal to A and read as ‘X’ does not
belongs to ‘A’ or ‘x’ is not an element of ‘A’ or
‘x’ is not in A. Example A= (1,2,3,4,) then 3 is
= A But 2 is not = to a.

6. TYPES and KINDS OF SET
• (a). Finite set = A set is said to be finite set if the
number of elements in it is finite . example A=
(Delhi , Kolkata)
• (b). Infinite set = A set is said to be infinite set if
the elements of the set are infinite or unlimited .
Example A=(1,2,…..).
• (c) Null set = A set is said to be null if no element
belongs to it. Example =( ).
• (d) singleton set = A set consisting of single
element is called singleton set. Example =A(1).
• (e) Disjoint set = if two set A and B have no
element in common ,is said to be disjoint set.
• Example = A(1,2,3,) B=(4,5,6,)

7. SUB -SET
• If two set A and B are that each element of A is
also an element of B , then set A is called a sub
set of the set B.
• EXAMPLE: A =(1,2,3,4,5,6,)
• B= (4,5,6,)
• IN THIS ‘A’IS NOT A SUB SET OF ‘
• ‘B’.

8. UNION OF SET

9. Intersection of set

10. DE-MORGANS LAW’S
• DE-MORGAN’S LAW are a pair of
transformation rules that are both valid of
inference. Its named after “Augustus De
Morgan” a 19th century British mathematician.