Gate2017 cs Q54

54Let A and B be infinite alphabets and let # be a symbol outside both A and B. Let f be a total functional from A* to B*. We say f is computable if there exists a Turning machine M which given an input x in A*, always halts with f(x) on its tape. Let L_f denote the language {x ≠ f(x) | x ∈ A*}. Which of the following statements is true:

Option : A
Explanation :
A TM is recursive iff it halts for every input string (either in accept or reject state). Here, a computable function is defined in a similar way.

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