Subset and Superset

           A set A is called a subset of B (or B is called the superset of A), denoted by , if all the elements of A are also elements of B. Thus .

           If A is a subset of B and there is at least one element in B which is not an element of A, then A is called a proper subset of B. We write

Example 2     Let .

           Then, .

• A  set   A   is a subset of itself   .
• implies that   .
• The null set is  a subset of every set.
• If the set A is finite with n number of elements, then A has subsets.
    For example,  the set of binary digits has subsets.
    These are:   .