SOLUTION: Consider the set B = {pen, pencil}. This set has subsets and proper subsets.

Its subsets are

1.  {} or ⌀, the empty or null set.
2.  (pen}
3.  {pencil}
4.  {pen, pencil}

There is only ONE improper subset, and that is the whole set,
{pen, pencil}.  It is not a proper subset because it is not
proper to label it "sub".

So the proper subsets are all those except the last one, the
whole set itself:

1.  {} or ⌀, the empty or null set.
2.  (pen}
3.  {pencil}

Edwin