Set theory
Set theory, it is a branch of mathematics which means a well - defined collection of objects or elements. The elements or the objects inside the set are known as the members of that set.
A set is represented by capital letter. The number of elements in a set is known as cardial number of set.
For example :
S = { 1, 2, 3, 4}
Here, S is the name of the set and ( 1, 2, 3, 4) are the elements of the set.
Types of sets
1 . Singleton set :
As the name indicates singleton set is a set which consists of only single element.
For example :
A = { 3 } , B = { d } here, A and B are sets which consists only single element ' 3 ' and ' d '.
2 . Empty set :
A set which contains no elements is known as empty set. It is denoted by Φ sign. The empty set is also called a null or a void set.
For example :
S = { Φ } , M = { } here, the set S and M does not contains any elements hence, these sets will be considered as empty set.
3 . Equal set :
When two sets contain same elements means, when every element of set A is in other set B and every element of set B is in set A. Then A = B will be considered as equal set.
For example :
A = { 1, 2, 3, 4, 5 } , B = { 4, 3, 2, 5, 1 } here A = B hence, it is a equal set.
4 . Finite set :
A set which consists of finite number of elements, means a set whose number of elements are countable is known as finite set.
For example :
A = { 1, 2, 3, 4, 5} here the set A consists 5 elements.
B = { a, b, c, d, e, f } here the set B consits 6 elements.
5 . Infinite set :
A set which consists of infinite number of elements, means the elements of the set are not countable is known as infinite set.
For example :
A = { 1, 2, 3, 4, ..... } here, the set A is a infinite set.
B = { 2, 4, 8,10, .....}here, the set B is a infinite set.
6 . Sub set :
A sub set can be defined as part of another set, the elements of B should also be in a set A. It is denoted using ⊆ sign. The ⊆ symbol is read as " is subset of ".
For example :
A = { 1, 2, 3, 4, 5}
B = { 2, 3, 4} , Here B ⊆ A or it can be read as B is subset of A.
7 . Power set :
The power set is known as the collection of all the subsets of any set. Here, the power set of A is denoted by P ( A ).
For example :
A = { 1 , 2, 3}
P ( A ) = { ( 1 ),( 2 ),( 3 ),( 1, 2 ),( 1, 3 ),( 2, 3 ),( 1, 2, 3 ),( Φ )}
8 . Universal Set :
A universal set can be known as the collection of all the elements of the given sets. It is usually denoted by U.
For example :
A = { 5, 6, 7, 8 }
B = { a, b, c, d, e }
U = { 5, 6, 7, 8, a, b, c, d, e } here it is the universal set for set A and B.
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