GATE 2022: Theory Of Computation Quiz-8

Which of the following problems is undecidable? 

Consider recursively enumerable language (RE) and following operations

1) Intersection

2) Substitution

3) Union

4) Kleene closure

5) Complementation

6) Reversal

 The number of operations under which RE is closed ____.

consider the following statements

Statement 1- If S1 and S2 are countable sets, then union of S1 and S2 is countable.

Statement 2- The cartesian product or union of finite countable sets may or may not be countable.

Statement 3- The set of all languages that are not recursively enumerable is uncountable.

Number of statements that are correct is ______.