GATE CSE 2014 Set 3 | Question: 16

Question

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

• A. Both $2^{\Sigma^*}$ and $\Sigma^*$ are countable
• B. $2^{\Sigma^*}$ is countable and $\Sigma^*$ is uncountable
• C. $2^{\Sigma^*}$ is uncountable and $\Sigma^*$ is countable
• D. Both $2^{\Sigma^*}$ and $\Sigma^*$ are uncountable

Comments

@Arjun sir, I think this should be added under TOC rather than Set Theory. 

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Arjun sir, I too think it should be in toc, countability.

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@Mk Utkarsh

a bijective mapping or one to one correspondence to natural numbers must be there for a set to be countable.

Answer 1

Option (C) 2^ (Σ *​​​​​​​)​​​​​​​ is uncountable and Σ *is countable ,is the correct answer.