The concept of subset is defined as, a set A is said to be the subset of a set B if every element of set A is also an element of set B, this relationship is usually denoted by and mathematically this relationship is written as, if implies . The concept of subset is also written in the from
If , in this case we say that A is contained in B or B contains A. If A is a subset of B and B has at least one element which is not in A, then A is called the proper subset of B. Proper subset more briefly id also defined as A is a proper subset of B if and .
If A is a subset of B, then B is called the super set of A. The symbol is called the inclusion symbol. If A is not a subset of B we write. By the definition of a subset it is clear that the empty set and the set A itself are always subsets of A. These two subsets are called the improper subsets of A.
If we have to show that A is a subset of B, then we take any arbitrary point of A and show that this point also lies in B. This will give us information that every point of A is also a point of B. Consequently we conclude that A is a subset of B. This concept can be explained as mathematically if implies.
The other way to prove that A is a subset of B is that we show that B is a super set of A. For this purpose, we consider an arbitrary point which is not in B and show that this point is also not in A. In this way we conclude that a point which is not in B is also not in A which shows that B is a super set of A.