Let \(Σ\) be a finite non-empty alphabet and let \(2^{Σ^*}\) be the power set…

GATE · 2014 · CS · Set 3 · Computer Science & IT

1. A.

   Both $2^{Σ^∗}$ and $Σ^*$ are countable

2. B.

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

3. C.

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

4. D.

   Both $2^{Σ^∗}$ and $Σ^*$ are uncountable

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