Correct Answer - Option 3 : 2∑*
is uncountable and ∑* is countable
Set of all strings over any finite alphabet are countable. Therefore, ∑* is countable.
Moreover, a set is countable if there exists an enumeration procedure to generate each of its elements and for a given element of set, it takes finite step to generate it using the enumeration procedure.
Note that, ∑* is countable but it is countably infinite.
According to Diagonalization Method, If ∑* is countably infinite then 2∑* is uncountable