# GATE Papers >> CSE >> 2019 >> Question No 15

Question No. 15

Let $U=\{1,2,\;...\;,\;n\}.$ Let $A=\{(x,\;X)\;\vert x\in X,\;X\subseteq U\}.$ Consider the following two statements on |A|.

I.  $\vert A\vert=n2^{n-1}$

II. $\vert A\vert={\textstyle\sum_{k=1}^n}k\begin{pmatrix}n\\k\end{pmatrix}$

Which of the above statements is/are TRUE?

##### Answer : (C) Both I and II

Solution of Question No 15 of GATE 2019 CSE Paper

Both I and II are equivalent statements.

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