## Thinking Mathematically (6th Edition)

The formula is $2^n-1$. For example, the set {A, B, C} has $2^3-1=7$ proper subsets.
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. $2^3-1=7$