Problem 7 (6 points)
(a) Give an example of a context-free language whose complement is not context-free. Give a precise definition of this language and explain your answer. If such a language does not exist, explain why.
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(b) Give an example of a regular language that has a subset which is not context-free. Give a precise definition of both languages and explain your answer. If such a language does not exist, explain why.
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(c) Give an example of a recursive language whose complement is not recursively enumerable. Give a precise definition of this language and explain your answer. If such a language does not exist, explain why.
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(d) Give an example of a recursively enumerable language whose complement is not recursively enumerable. Give a precise definition of this language and explain your answer. If such a language does not exist, explain why.
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