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Gate CS-2014-3 Question Paper With Solutions

Q. 26 Let $Σ$ be a finite non-empty alphabet and let $2^{Σ^{*}}$ be the power set of $Σ^{*}$ . Which one of the following is TRUE?

(A)Both $2^{Σ^{*}}$ and $Σ^{*}$ are countable

$2^{Σ^{*}}$ is countable and $Σ^{*}$ is uncountable

$2^{Σ^{*}}$ is uncountable and $Σ^{*}$ is countable

(D)Both $2^{Σ^{*}}$ and $Σ^{*}$ are uncountable

Answer: (C)

Explanation:

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