Set
Theory
- Representation of a Set
- Types of Sets
- Finite Sets and Infinite Sets
- Power Set
- Problems on Union of Sets
- Problems on Intersection of Sets
- Difference of two Sets
- Complement of a Set
- Problems on Complement of a Set
- Problems on Operation on Sets
- Word Problems on Sets
- Venn Diagrams in Different Situations
- Relationship in Sets using Venn Diagram
- Union of Sets using Venn Diagram
- Intersection of Sets using Venn Diagram
- Disjoint of Sets using Venn Diagram
- Difference of Sets using Venn Diagram
- Examples on Venn Diagram
Set Definition
is
a
- Odd Numbers less than 20, i.e., 1, 3, 5, 7, 9, 11, 13, 15, 17, 19
- Prime Factors of 15 are 3, 5
- Types of Triangles depending on Sides: Equilateral, Isosceles, Scalene
- Top two surgeons in India
- 10 Famous Engineers of the Society.
branch
of
mathematics
and
is
a
collection
of
objects
known
- Statement Form
- Roaster Form or Tabular Form
- Set Builder Form
Statement Form: In this representation, elements of the set are given with a well-defined description. You can see the following examples for an idea
Example:
as
numbers
Roaster Form or Tabular Form: In Roaster Form, elements of the set are enclosed within a pair of brackets and separated by commas.
or
elements
of
Set Builder Form: In this representation, Set is given by a Property that the members need to satisfy.
the
set
.
Set
can
be
Finite Set: A Set containing a finite number of elements is called Finite Set. Empty Sets come under the Category of Finite Sets. If at all the Finite Set is Non-Empty then they are called Non- Empty Finite Sets.
defined
Infinite Set: In Contrast to the finite set if the set has infinite elements then it is called Infinite Set.
as
Power Set: Power Set of A is the set that contains all the subsets of Set A. It is represented as P(A).
a
collection
Sub Set: If Set A contains the elements that are in Set B as well then Set A is said to be the Subset of Set B.
of
elements
enclosed
Universal Set:
within
curly
Empty Set:
brackets
.
Singleton Set:
Set
can
be
denoted
Union: Union Operation is given by the symbol U. Set A U B denotes the union between Sets A and B. It is read as A union B or Union of A and B. It is defined as the Set that contains all the elements belonging to either of the Sets.
Intersection: Intersection Operation is represented by the symbol ∩. Set A ∩ B is read as A Intersection B or Intersection of A and B. A ∩ B is defined in general as a set that contains all the elements that belong to both A and B.
Complement: Usually, the Complement of Set A is represented as A c or A ‘ or ~A. The Complement of Set A contains all the elements that are not in Set A.
Power Set: The power set is the set of all possible subsets of S. It is denoted by P(S). Remember that Empty Set and the Set itself also comes under the Power Set. The Cardinality of the Power Set is 2 n in which n is the number of elements of the set.
Cartesian Product: Consider A and B to be Two Sets. The Cartesian Product of the two sets is given by AxB i.e. the set containing all the ordered pairs (a, b) where a belong to Set A, b belongs to Set B.
using
three
