Definition Subset

Sub-set means part of. If we say that America is part of world then America is said to be sub-set of world. So we Define Subsets as the set which is part of another set. For example in library are many book shelves according to the subjects.
Consider a book shelf containing English books. Then the English book shelf will be sub-set of all library shelves.
Consider students in your class which makes a set C and all students in your school which makes a set S. the set C will be sub-set of set S as it is a part of set S or we can say it is contained in set S.  :

Definition Subset / Subsets Definition – sub-sets are those sets whose all elements are contained in some another set.

Let us see properties of sbsets:
Symbol used for sub-set is:  or . Example if A is sub-set of B then we write it as: A B or A B.
A sub-set may be sub-set of more than one set. For example: consider set N = {11, 33, 77}. This set can be sbset of any set containing the elements 11, 33 and 77 like {1, 2, 11, 33, 77}, {a, e, 33, 11, 77} and many more.
All sets are sub-set of themselves. For example set S={English, math, science, GK}. Then the set S contains these elements. We can say that S is sub-set of S.

An empty set (φ) is sub-set of itself and also sub-set of all other sets.
A set is said to be proper sub-set of another set if another set contains the sub-set and also one or more extra elements with it. For example: set A = {c, v, r, e, m} is proper sub-set of B = {c, v, r, e, m ,s} as it contains extra elements s with the elements of A. A set can be proper sub-set of more than one set. For example above set A is also proper sub-set of C ={c, v, r, e, m, d, s, a}. Null set is proper sub-sets of all the existing sets.

If A is sub-set of set B then B is known as super set of B.

A superset can also be sub-set of some other set.

If A is sub-set of B and B is also sub-set of A, then A is equivalent set of B or A=B.

Possible Number Subsets in set A = 2n where n is number of elements in set A.
These are the properties of Subsets Math