Let π‘ˆ = {1,2, … , 𝑛}. Let 𝐴 = {(π‘₯, 𝑋)|π‘₯ ∈ 𝑋, 𝑋 βŠ† π‘ˆ}. Consider the…

GATE Β· 2019 Β· CS Β· Computer Science & IT

Let π‘ˆ = {1,2, … , 𝑛}. Let 𝐴 = {(π‘₯, 𝑋)|π‘₯ ∈ 𝑋, 𝑋 βŠ† π‘ˆ}. Consider the following two statements on |𝐴|.

I.     ∣A∣=n2nβˆ’1\mid A \mid = n2^{n-1}

II.    ∣A∣=Σk=1nk(nk)\mid A \mid = \Sigma_{k=1}^{n} k \begin{pmatrix} n \\ k \end{pmatrix}

Which of the above statements is/are TRUE?

  1. A.

    Only I

  2. B.

    Only II

  3. C.

    Both I and II

  4. D.

    Neither I nor II

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