Question

whats the fastest and most easiest way to find all the subsets in a given set?

Answer 1

use 2 as the base!, 2 raise to the power of n, where n is the number of elements in a set.

Answer 2

The power set is the set of all possible subsets of a given set of cardinality n (contains n elements). The power set has a cardinality of 2^n.

To find the all elements of the power set of a given set A, we start with the null set, and add one element at a time.
{∅}
{∅,a}
{∅,a, b,{a,b}}
{∅,a, b,{a,b}, c,{a,c},{b,c},{a,b,c}}
...
and so on.

We see that the introduction of each element of A doubles the number of subsets, hence the total number of 2^n.