1:) i dont know what is the meaning of[0,1]..if it is all real nos between 0 to 1 then yes we cant design an enumerator for this..as it is uncountable
2:)we know that set of all strings generated by an alphabet is countable....also set of all languages is not countable(can be proved using diagnolisation method)...so this statement is also false
3:)obviously no...we need some method to enumerate one to one correspondence of all real nos with natural nos...but it is not possible...between 0 and 1 only we have so many real nos which will literally eat up all natural nos
(Now i dont know the difference between option 1 and this option)
4:)yes....since sigma star is countable...and we know that set of all TM is a subset of sigma star....means subset of a countable set is countable....so this is true...
final conclusion:....b and c are definitly wrong.....d is true...i dont know what is a option means...