Let ∑ be a finite non-empty alphabet and let 2∑*

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

1. Both 2^∑* and ∑* are countable
2. 2^∑* is countable and ∑* is uncountable
3. 2^∑* is uncountable and ∑* is countable
4. Both 2^∑* and ∑* are uncountable

∑* is countabily finite 2∑* is power set of ∑*
The powerset of countabily infinite set is uncountable
∴ 2∑* is uncountable and ∑* is countable.