a set of n elements has 2^n -1 proper subsets
255 = 2^8 - 1
255 = 2^8 - 1
n(A) = 2^k
Where n(A) represents the number of elements in set A, and k represents the number of elements in set A's power set.
Since A has 255 proper subsets, we need to find the value of k.
The power set of A includes all possible subsets of A, including the empty set and A itself. However, since we are looking for proper subsets (excluding the empty set and A), we need to subtract 2 from the number of subsets to obtain the value of k.
k = 255 + 2
k = 257
Now, we can substitute the value of k into the formula:
n(A) = 2^257
However, it is worth noting that 2^257 is an extremely large number, which means that set A would have an impractically large number of elements. It is possible that there may be an error in the initial question or the context in which it is presented.