Is it true that every recursively enumerable language is recursive, and is it true that every language is recursively enumerable?
Answer)
When the language is recursive, there will exist the Turing machine
which can accept or reject the language. The recursive languages
will be the subset of recursively enumerable, thus the Turing
recognizable means that the language is also recursively
enumerable. Thus it is true that the recursively enumerable
language or the recursive languages are always recursively
enumerable.
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