What is the difference between a subset and a proper subset?

A subset is a set that contains all the elements of another set, including the possibility of being equal to the other set. In other words, if every element of set A is also an element of set B, then A is a subset of B.

On the other hand, a proper subset is a subset that contains all the elements of another set, but it is not equal to the other set. In other words, if every element of set A is also an element of set B, but there exists at least one element in set B that is not in set A, then A is a proper subset of B.

To summarize, the main difference between a subset and a proper subset is that a proper subset does not include all the elements of the other set, while a subset can include all the elements.