Find examples of languages satisfying each of the following properties (briefly justifying why they do), or prove that no such language exists.

(a) An unrecognizable language whose complement is finite.

(b) A context-free language that is undecidable.

(c) A recognizable language with an unrecognizable subset.

(d) An undecidable language that is recognizable.

(e) An undecidable language that is unrecognizable.