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## Q.62) Let 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 Lf denotes the language {x#f(x)|x∈A*}. Which of the following statements is true? -gate computer science 2017

*A) f if computable if and only if Lf is recursive.*

*B) f if computable if and only if Lf is recursive enumerable.*

*C) if f is computable then Lf is recursive, but not conversely.*

*D) if f is computable then Lf is recursively enumerable, but not conversely.*By:satyashiromani

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## Answers

**A) f if computable if and only if Lf is recursive.**

Explanation:

This definition is given as Halting of Turing Machine. Every recursive language is computable, but converse may not be true.

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