Explanation
A = {(x, X), x ∈ X and X ⊆ U}
The number of k element subsets of a set U with n elements
The number of possible ordered pairs (x, X) where x ∈ X is k ⋅ nCk for a given value of k from 1 to n.
So total number of ordered pairs in A
So II is correct.
(Note that k = 0 is excluded since empty set has no elements and cannot form an order pair such as (x, X)).
But since by the combinational identity
So I is also correct.
So both I and II are correct.