Different Types Of Set

Sets may be of vatrious types. we give below a few of them...
Finite Set:
When the elements of a set can be counted by finite number of elements then the set is called a finit set. The following are the examples of finite sets:

In all above sets the elements can be counted by a finite number. It should br denoted that a set containing a very large number of elements is also a finite set. Thus, the set of all human beings in india, the set of all integers between -1 crore and +1 crore all finite sets.

Infinite Set:
If the elements of a set can not be counted in a finite number, the set is called an infinite set. The following are examples of infinite sets:

In all above sets, the process of counting the elements would be endless, hence these are infinite sets.

Singleton:
A Set containing only one element is called a singleton or a unit set. For example...

Empty, Null Or Void Set:
Any set which has no elements in it is called an empty set, or a null set or a void set. The symbol used to denote an empty is a Greek letter (read as phi), i.e., zero with a slish through it. Here the rule or the property discribing a given set is such that no element can be included in the set. The following are a few examples of empty sets:

Thus a we may say that laying down an impossible condition for the formation of a set produces an empty set.

Equal Set:
Two sets A and B are said to be equal if every element of A is also an element of B, and every element of B is also an element of A , i.e.,
We find that A=B=C, as each set contains the same elements namely a, c, h, m, r irrespective of their order. Hence the sets are equal. It may be noted that the order of elements or the repetition of elements does not matter in set theory.

Equivalent Sets:
If the elements of one set can be put into one to one correspondence with the elements of another set, then the two sets are called equivalent sets. For example..
Here A and C are equal sets while A and B are equivalent sets.

Subsets:
If every element of a set A is also an element of a set B then set A is called subset of set B. Symbolically we write this relationship as..

Proper Set:
Set A is called proper subset of superset B if each and every element of set A are the elements of the set B and at least one element of superset B is not an element of set A. Symbolically this is written a ACB and is read as 'A is a proper set of superset B'

Family Of Sets:
If all the elements of a set are sets themselves then it is called a 'set of sets' or better term is a 'family of sets'

Power Set:
From a set containing n elements 2n subsets can be formed. The set consisting of these 2n subsets is called a power set. In other words, if A be a given set then the family of sets each of whose number is a subset of the given set A called the power set A and is denoted as P(S), For example..

Universal Set:
When analysing some particular situation we are never required to go beyond some particular well-defined limits. This particular well-difined set may be called the universal set for the particular situation. Now onwords, we will assume that we are well aware of the particular universal set under consideration. The universal set will generally be denoted by the symbol 'U'