2. A set is a well defined collection of
objects.
Sets are usually denoted by capital
letters A, B, C, X, Y, Z.
The elements of a set are represented by
small letters a, b, c, x , y , z etc.
3. Different Types Of Sets
The Empty Set
Finite and Infinite Sets
Equal Sets
Subsets
Power Set
Universal Set
4. The Empty Set
A set which does not contain any element
Which is also called null set or void set
It is denoted by ɸ or { }
Example : C = { x: 1 < x < 2 ,x is a natural number}.Then
C is the empty set ,because there is no natural number
between 1 and 2
5. Finite and Infinite Sets
A set which is empty or consists of a definite number of
elements is called finite set .
Otherwise , the set is called infinite set .
Example:
(ⅰ) Let W be the set of the days of the week.Then W
is finite.
(ⅱ) Let G be the set of points on a line. Then G is
infinite
6. Equal Sets
Two sets A and B are said to be equal if they have
exactly the same elements otherwise, the set are said
to be unequal.
A ={ 1, 2 , 3,4 } and B ={ 4, 2, 1, 3 } then, A= B
7. Subsets
A set ' A' is said to be a subset of 'B' if every element of
A is also an element of B
It is denoted by A Ϲ B
8. Power Set
The collection of all subset of a set A is called the power
set of A.
It is denoted by P(A)
A ={1, 2} then, P(A) = {ɸ, {1}, {2}, {1,2} }
9. Venn Diagram
Most of the relationship between sets can be represented
by means of diagrams which are known as Venn diagram.
Venn diagram are named after the English logician, John
Venn (1834-1883).
It consists of rectangles and closed curves usually circles.
