CHAPTER:1 SETS
WHAT IS SET
A set is a well-defined collection of objects.
REPRESENTATION OF SETS
There are two methods of representing a set
1.Roster or Tabular form In the roster form we list all the members of the set within braces { }
and separate by commas.
2.Set-builder form In the set-builder form we list the property or properties satisfied by all the
elements of the sets.
TYPES OF SET
1.Empty Sets: A set which does not contain any element is called an empty set or the void set or
null set and it is denoted by {}.
2.Singleton Set: A set consists of a single element, is called a singleton set.
3.Equal Sets: Two sets A and B are said to be equal, if every element of A is also an element of B
or vice-versa, i.e. two equal sets will have exactly the same element.
4.Equivalent Sets: Two finite sets A and B are said to be equal if the number of elements are
equal, i.e. n(A) = n(B)
5.Finite Set:
6.Infinite Set: The set which is not finite is called infinite set
SUBSETS
A set A is said to be a subset of set B if every element of set A belongs to set B.
Note:
-> Every set is a subset of itself.
-> The empty set is a subset of every set.
-> n define the number of elements in a finite set
-> The total number of subsets of a finite set containing n elements is 2n
Power Set: The collection of all subsets of a set A is called the power set of A. It is denoted by
P(A). If the number of elements in A i.e. n(A) = n, then the number of elements in P(A) = 2n.
Universal Set: A set that contains all sets in a given context is called the universal set.
Venn-Diagrams: Venn diagrams are the diagrams, which represent the relationship between sets.
In Venn-diagrams the universal set U is represented by points within a rectangle and its subsets
are represented by points in closed curves (usually circles) within the rectangle.
OPERATION OF SETS
WHAT IS SET
A set is a well-defined collection of objects.
REPRESENTATION OF SETS
There are two methods of representing a set
1.Roster or Tabular form In the roster form we list all the members of the set within braces { }
and separate by commas.
2.Set-builder form In the set-builder form we list the property or properties satisfied by all the
elements of the sets.
TYPES OF SET
1.Empty Sets: A set which does not contain any element is called an empty set or the void set or
null set and it is denoted by {}.
2.Singleton Set: A set consists of a single element, is called a singleton set.
3.Equal Sets: Two sets A and B are said to be equal, if every element of A is also an element of B
or vice-versa, i.e. two equal sets will have exactly the same element.
4.Equivalent Sets: Two finite sets A and B are said to be equal if the number of elements are
equal, i.e. n(A) = n(B)
5.Finite Set:
6.Infinite Set: The set which is not finite is called infinite set
SUBSETS
A set A is said to be a subset of set B if every element of set A belongs to set B.
Note:
-> Every set is a subset of itself.
-> The empty set is a subset of every set.
-> n define the number of elements in a finite set
-> The total number of subsets of a finite set containing n elements is 2n
Power Set: The collection of all subsets of a set A is called the power set of A. It is denoted by
P(A). If the number of elements in A i.e. n(A) = n, then the number of elements in P(A) = 2n.
Universal Set: A set that contains all sets in a given context is called the universal set.
Venn-Diagrams: Venn diagrams are the diagrams, which represent the relationship between sets.
In Venn-diagrams the universal set U is represented by points within a rectangle and its subsets
are represented by points in closed curves (usually circles) within the rectangle.
OPERATION OF SETS
