Question

If n (p(a) = 1024 find (n(a)

Answer 1

The power set of a set has always a power of 2 as its cardinality. And it's not any power of 2, it's 2 raised to the cardinality of the normal set.

If a set A has a cardinality of 'n', then its power set P(A) has a cardinality of '2^n'.

In short, if n(A) = n, then n(P(A)) = 2^n.

Here, given that n(P(A)) = 1024.

Let n(A) = n. We have to find this 'n'.

So n(P(A)) becomes 2^n.

    2^n = 1024

⇒  2^n = 2^10

⇒  n = 10.

Thus the set A has a cardinality of 10. Means A has 10 elements.

Remember! Sets are usually denoted by capital letters! That's why 'a' is taken as 'A' here!