If A and B are sets, and if every element of A is an element of B,
we say that A is a subset of B,
and write A⊂B .
If, in addition,
there is an element of B which is not in A,
then A is said to be a proper subset of B
in short
If A = {1,2} and B= {1}..
A subset can be the set itself, like A is a subset of A or B is a subset of A. A subset means that it is contained within something.
A proper subset on the other hand means that the subset is not the set itself. So A is not a proper subset of A. Taking the above example and that B is not A, then B would be a proper subset of A.