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second one is uncountable?

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All regular languages are countable sets of words. Finite languages are trivially countable. Infinite languages are countable because the corresponding DFA can be walked over, enumerating the entire language in an ordered manner, allowing all strings to be mapped to the natural numbers.

 

So,

  • Though powerset is not countable for all sets,but power set of Natural number  and integer are countable
  • Though if there are possibility of rational number , it will be uncountable infinite set

So, here 1st one is finite set and 2nd one power set of Natural number, which are integer. So, both (i) and (ii) need to be countable

Ref:https://stackoverflow.com/questions/52567805/can-countable-string-is-countable-always

https://cs.stackexchange.com/questions/97914/is-countable-set-always-countable?noredirect=1#comment208658_97914

  

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