Question

If n(p(a)=256, find n(a)

Answer 1

Let A be a set

So, we know n(A) is called cardinal number of the set A which is equal to 
number of elements in set A and
p(A) is called power set of A.

Power set p(A) = set of all subsets of set A

We also know that,
If number of elements in set A = n then, n(A) = n

and Number of subsets of power set = 2^n

So equating values, we get
2^n = 256
2^n = 2^8
so, n = 8
Therefore, Number of elements in set A, n = 8