Given S = {a, b}, which one of the following sets is not countable?
A)the set all strings over ?
B)the set of all language over ?
C)the set of all binary strings
D)the set of all languages over ? accepted by turing machines

Question

Quizplus · Accepted Answer

The set of all languages over S is not countable because for any set, the set of all possible subsets (the power set) is always larger than the set itself. Since S is countable, the set of all subsets (languages in this context) of S is uncountable, as there is no one-to-one correspondence between the set of all languages and the natural numbers.

Given S = {A, B}, Which One of the Following