Answer
The formula is $2^n-1$.
For example, the set {A, B, C} has $2^3-1=7$ proper subsets.
Work Step by Step
The formula for finding the number of distinct subsets for a given set with $n$ distinct elements is:
$2^n$
The only subset that also isn't a proper subset is equal to the set itself.
Therefore, each set has one less proper subset than it has subsets.
The formula for a set with $n$ elements is: $2^n-1$
An example would be:
{A, B, C}
The proper subsets are:
{A, B}
{A, C}
{B, C}
{A}
{B}
{C}
{}
There are 7 of them. The set has 3 elements.
$2^3-1=7$
