Question

Which of the following statements are false?

(a) Every recursive language is recursively ennumerable

(b) Recursively ennumerable language may not be recursive

(c) Recursive languages may not be recursively ennumerable

(d) None of the mentioned

This question was posed to me in final exam.

Asked question is from The Language of Turing Machine-2 in section Introduction to Turing Machines of Automata Theory

Answer 1

The correct answer is (c) Recursive languages may not be recursively ennumerable

Easiest explanation: Every recursive language is recursively ennumerable but there exists recursively ennumerable languages  that are not recursive. If L is accepted by a Non deterministic TM  T, and every possible sequence of moves of T causes it to halt, then L is recursive.