The power of a set with k elements is
The power of a set with k+1 elements is
Show that P(k+1) must be true if P(k) is true.
If a set of k elements has a power of
then an added element will form new subsets as it can be placed with all existing subsets.
Therefore a set of k+1 elements has a power of if a set of k elements has power
Finally prove for the base case.