7,651 views

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

1. Both $2^{\Sigma^*}$ and $\Sigma^*$ are countable
2. $2^{\Sigma^*}$ is countable and $\Sigma^*$ is uncountable
3. $2^{\Sigma^*}$ is uncountable and $\Sigma^*$ is countable
4. Both $2^{\Sigma^*}$ and $\Sigma^*$ are uncountable

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

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

edited

@Mk Utkarsh

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

by