The Chomsky hierarchy of language classes and the corresponding machines that decide them.
Regular languages are the simplest. L is regular if and only if there exists a deterministic finite state automaton M that decides L.
Also, L is regular if and only if there exists a nondeterministic finite state automaton M that decides L. Finally, L is regular if and only if there exists a regular expression E such that E generates a string w if and only if w is an element of L.
All regular languages are context free. L is context free if and only if there exists a nondeterministic pushdown automaton M that decides L. (Note: The class of languages decided by deterministic pushdown automata is a strict subset of the class of context free languages.)
L is context free if and only if there exists a context free grammar G such that G generates a string w if and only if w is an element of L.
All context free languages are recursive. L is recursive if and only if there exists a Turing machine M that decides L. (It appears that the decidable languages are not technically a member of the Chomsky hierarchy, but they fit in there nicely.)
All recursive languages are recursively enumerable. L is recursively enumerable if and only if there exists a Turing machine M that recognizes L.
Choice B is not true because if L is recognized by Turing machine M, then this only implies that L is recursively enumerable. It does not imply that L is recursive, since M might not be able to decide L.