The proper subsets of a set are all subsets, including the null set, except the one subset that is identical to the given set.
You need the number of ways to select 0 things from 3 things, plus
The number of ways to select 1 thing from 3 things, plus
The number of ways to select 2 things from 3 things, but exclude
The number of ways to select 3 things from 3 things.
Where is the number of combinations of things taken at a time and is calculated by
Hint: Look at the 4th row of Pascal's triangle, and exclude the last element.
Now that you know the total number of proper subsets, you can determine if you have listed all of them and you can determine if you have made any duplications.
John
My calculator said it, I believe it, that settles it
