Subset

So what is the basic difference between a set and a sub-set? The answer is simple. A set has all the elements that are present in  a subset but a subset. does not contain all the elements of a set, it contains only a few elements. But it crucial to note that a subset. of a particular set will have no element that is other then what is present in that set.

So a subset. is a smaller or condensed form of a set. Let us consider a set of integers less than 5 and greater than 1. A = {  2,3,4 } now B which is a subset. of A can be any one of these: B = { 2,3} or B = {2} or B = { 3,4} etc. but not that B has no element other than that of A.

Even a null set is a sub-set of all the set may it be any set. A set of numbers can be either a set of real numbers or a set of integers or a set of fractions or a set of floating point number etc.  A set of numbers hence can be considered as a superset of all the other sets. A super set is which that contains all the sets elements of the given sub-sets. In the above example A can be called a superset of B and B can be called a S. S of A or just Subsets of Numbers.

The sum of subsets of a particular set will make up that set. It should be noted that null set belongs to every set.
To explain the Subsets of integers we can take up another example. The subsets can be A (sub-set of I) : { -1, -2 , 0 ,1, 2, 3} etc. All subsets are the part of a universal set which contains all the numbers. For a S. s of a integer we can have as many numbers as there are integers and then we can add a null set to it to get the original set.

The Set and Subset are the essentials for analyzing particular type of data and hence should be understood very clearly. The proper set and the improper set are yet another types of set, in a proper set we also have null element or entity. Similarly we can define s. s. for the same set.
R denotes the set of real numbers. Say ‘r’ is a s. s. of real numbers we write it as r = {0}