Recursive Language:

Let L be a language over an input and if TM 'T' (Turing machine T) excepts every woed in L and rejects every word of L' it is called as recursive language.

Example:

1. String ends with '101'

2. Number of 'a'= number of 'b'

   Accept(T) = L

   Reject(T) = L'

   Loop(T) = ϕϕ

   ϕ = nullϕ = null

Recursive enumeration language:

Let L be a langauage over an input, and if TM 'T' excepts every word of L and rejects or loops every word in L' then it is called recursive enumeration language.

Example:

$a^nb^n$

Accept(T) = L

Reject(T) + Loop(T) = L'