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2. (10 points) Find examples of languages satisfying each of the following properties (briefly jus- tifying why they do), or prove that no such language

2. (10 points) Find examples of languages satisfying each of the following properties (briefly jus- tifying 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.

2. (10 points) Find examples of languages satisfying each of the following properties (briefly jus- tifying 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 2. (10 points) Find examples of languages satisfying each of the following properties (briefly jus- tifying 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

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