# Is it true that every recursively enumerable language is recursive, and is it true that every...

Is it true that every recursively enumerable language is recursive, and is it true that every language is recursively enumerable?

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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