Let 𝑈 = {1,2, … , 𝑛}. Let 𝐴 = {(𝑥, 𝑋)|𝑥 ∈ 𝑋, 𝑋 ⊆ 𝑈}. Consider the following two statements on |𝐴|

Q.	Let 𝑈 = {1,2, … , 𝑛}. Let 𝐴 = {(𝑥, 𝑋)|𝑥 ∈ 𝑋, 𝑋 ⊆ 𝑈}. Consider the following two statements on |𝐴|. I.           |𝐴| = 𝑛2𝑛−1 II.         |𝐴| = ∑𝑛𝑘=1     𝑘(𝑛)            Which of the above statements is/are TRUE?
	(A) Only I	(B) Only II
	(C) Both I and II	(D) Neither I nor II

Given, A = {(x, X)∣ x∈X, X⊆U }, where U = {1, 2, …,n}.

As we know that The number of k element subsets of a set U with n elements = ⁿC_k.

The number of possible ordered pairs (x, X) where x ∈ X is k⋅ ⁿC_k for a given value of k from 1 to n. So total number of ordered pairs in A,