Determine whether the following statements are True or False. Provide sufficient reasoning in either case.

a) Every language has at least one TM that recognizes it.

b) If a TM recognizes some language L, then there is at least one string not in L that results in the TM failing to halt.

c) If a language is turing-unrecognizable, then for any M that attempts to do so, there must exist strings in L for which M does not halt.